A Mass, Fuel, and Energy Perspective on Fixed-Wing Unmanned Aerial Vehicle Scaling

Abstract

Fixed-Wing Unmanned Aerial Vehicles (UAVs) have been improving significantly in application and versatility, sharing design similarities with airplanes, particularly at the design stage, when the take-off mass is used to estimate other characteristics. In this work, an internal database of UAVs is built to allow their comparison with airplanes under different parameters and assess key differences in patterns across UAV powertrains. The existing literature on speed vs. take-off mass is updated with 534 UAV entries, and a range vs. take-off mass diagram is created with 503 UAVs and 193 airplanes. Additionally, different transportation efficiency metrics are compared between UAVs and airplanes, highlighting scenarios advantageous for UAVs. A new paradigm focused on useful energy is then used to understand the underlying effectiveness of UAV implementations. Increasing useful energy is more effective in increasing the speed, transport work, and surveying work of internal combustion UAVs and more effective in increasing the range and endurance of battery-electric UAVs. Finally, it is observed that the mass of all fixed-wing aerial vehicles, both UAVs and airplanes, except for battery electric and solar, adheres to a well-defined scaling law based on useful energy. A parallel to this scaling law is suggested to describe future battery-electric UAVs and airplanes.

1. Introduction

A Fixed-Wing Unmanned Aerial Vehicle (UAV) is a vehicle designed and used to transport cargo or survey an area by traversing a certain distance at a certain speed. Its performance in these tasks is influenced by various factors, including the aerodynamic characteristics of the vehicle, its structural mass, the payload being carried, the specifics of the powertrain, and the energy carrier supplying the powertrain. Moreover, the interplay between these components significantly affects the vehicle characteristics.

The relationships between the different characteristics are usually expressed as scaling laws as a function of mass; a detailed example for UAVs is given by Verstraete et al. [1], who characterized many geometrical and mass parameters of UAVs. These different scaling laws can be applied to estimate different characteristics of a UAV beginning at the conceptual level. However, the topic of energy storage and its impact on the UAV was not discussed in detail. This omission is particularly significant, as the energy storage capacity can significantly influence a UAV’s range and speed.

Conversely, Gurevich and Arav [2] evaluated the case of hybridizing a UAV, considering the energy it carried and its mass. In their reasoning, they anchored their conceptualization on the understanding from Bejan et al. [3] of the balance between the masses of the components, in their work, the propulsion system, and the mass of the vehicle itself, while contributing some UAVs to the grand diagram of motion from Bejan et al. [3] (speed as a function of mass).

This work by Bejan et al. [3] evidenced some critical aspects of these correlations, which, although directed at airplanes, are reasoned to be transferable across entities, biological or not. One of these critical aspects was that airplane implementations had developed over time toward specific and optimal ratios defined by the environment in which they moved. The previously mentioned balance is the anchor in these ideal proportions. Finally, they also reasoned that the range and speed of airplanes increase with their mass.

The insight into the similarity across entities in the same medium is shared by Sliwinski et al. [4], who considered the potential of UAVs as platforms for technological testing and development, with the objective of innovating aerial propulsion systems toward the development of similar solutions for airplanes. They justified this approach by demonstrating a hybridization scenario with an internal combustion and battery-electric system and analyzing the impact of varying the battery energy.

Remembering that the objective of UAVs, and of transportation systems in general, is to transport cargo, Gucwa and Schäfer [5] performed an analysis focused on the energy intensity of different transport systems from an efficiency point of view. Energy intensity, defined as total energy (equivalent to energy at the pump) per unit of cargo and distance, was evaluated using the available statistical data on road, rail, sea, and air vehicles. This analysis demonstrated that the energy intensity of the different transport systems decreases with the size of the vehicle and with the size of the cargo, thereby evidencing economies of scale across transportation systems.

It is the objective of the present article to build on the broad ideas from Bejan et al. [3] and Gucwa and Schäfer [5] and apply them to UAVs, specifically the former’s ideas on the conformation of the vehicle to the environment, so as to better understand and compare UAVs and airplanes, and the latter’s ideas on the use of energy, applying them to UAVs but from an exploratory perspective in which, for the first time, the efficiency is included in the analysis. We aim to show the impact of adopting efficiency when analyzing the characteristics of these machines while also analyzing the impact of the different powertrains on them.

Research Methods and Data

However, comparing airplanes and UAVs requires defining a coherent framework, especially as they can depend on different forms of energy (liquid fuel, gaseous fuel, or batteries) and powertrains to convert the energy into movement. Indeed, the powertrain is a critical element, as seen in Figure 1, where it is possible to see that a simple comparison of mass removes detail, as the differences in energy density (available energy column) and the specific impact of the powertrain components (energy conversion column) are not considered. Additionally, in this process, it is necessary to understand some particularities of UAVs, which requires the use of other metrics, such as take-off mass, as in [1,2,3], and payload, as in [5].

To aid in this endeavor, we have assembled a new dataset of UAVs. We seeded the dataset with models and manufacturers from a small online dataset [6] and Jane’s All the World’s Aircraft: Unmanned 2018–2019 [7], accounting for less than 40% of the dataset models. Subsequently, we consulted the various UAV manufacturers to fill in the missing data and augment the dataset with newer models. Additional manufacturers that were not in these seed sources were also included. These UAVs were classified based on the powertrain installed and the specific fuel, thereby allowing for their classification.

Turbofan airplane data were obtained from Airbus and Boeing [8,9], while indicative turboprop airplane data were from Marinus [10]. Since this turboprop dataset only provided the range with the maximum payload, it was augmented with data for the range at maximum take-off and fuel masses, when possible.

2. UAVs in the Evolution Map

Both airplane and UAV manufacturers’ datasheets contain numerous data fields; however, unlike the airplanes’ datasheets, UAVs’ often exhibit a lack of consistency in nomenclature between manufacturers and reduced data availability, a fact clear even in professional data aggregators (e.g., [7]). For example, while speed can include maximum, cruise, loiter, and stall speeds, occasionally, one can also find typical cruise and maximum cruise speeds or maximum and typical loitering speeds. Other parameters, such as weights, can sometimes take other varied forms. The range is a different example, as it often refers to the limit of the communication system rather than the flight range, as discussed in this document and as noted by Verstraete et al. [1]. However, there are rare cases in which the range is the actual flight range, even though often under ferry operation.

To bypass this limitation of the ambiguously defined flight range, we will assume

$$L\approx u_{\mathrm{C}}\times h.$$

(1)

Here, L is the range in $\mathrm{k}\mathrm{m}$, $u_{\mathrm{C}}$ is the cruise speed of the UAV in $\mathrm{k}\mathrm{m} {\mathrm{h}}^{-1}$, and h is the number of hours the UAV can stay airborne. Although it is not possible to claim this estimate to be the actual range, it will provide a reasonable approximation for the analysis in this work. Moreover, this is in agreement with the standard deduction of Breguet’s range equation. Note that, independently of the altitude at which the UAV is intended to fly, the energy consumption of the remaining flight segments is not considered. These remaining flight segments, namely, take-off, climb, and landing, also vary significantly between implementations.

Our dataset is briefly presented in Appendix A,

Table A1. Brief dataset metrics before subsequent processing. The number of entries is the cell value, and in parentheses is the percentage of the vertical category, except for the count row, in which the percentage is of all UAVs. The bold entries in the parameter column denote primary categories for the subsequent non-bold metrics. Note that the value of each row considers a UAV having this value but does not assume that other characteristics were available. Hence, the minimum number of entries can be calculated via the intersection formula for sets.

Parameter	All	Battery Electric	Fuel Cell	Generator	Internal Combustion	Solar	Turbine	Unspecified
Count	862 (100%)	302 (35%)	27 (3%)	6 (1%)	409 (47%)	18 (2%)	53 (6%)	47 (5%)
Maximum take-off mass	759 (88%)	282 (93%)	18 (67%)	6 (100%)	373 (91%)	15 (83%)	41 (77%)	24 (51%)
Payload mass	455 (53%)	149 (49%)	11 (41%)	2 (33%)	245 (60%)	6 (33%)	33 (62%)	9 (19%)
Endurance	769 (89%)	281 (93%)	21 (78%)	5 (83%)	380 (93%)	14 (78%)	41 (77%)	27 (57%)
Maximum speed	603 (70%)	220 (73%)	9 (33%)	3 (50%)	310 (76%)	8 (44%)	32 (60%)	21 (45%)
Cruise speed	563 (65%)	212 (70%)	14 (52%)	3 (50%)	286 (70%)	10 (56%)	26 (49%)	12 (26%)
Propulsion system	815 (95%)	302 (100%)	27 (100%)	6 (100%)	409 (100%)	18 (100%)	53 (100%)	—
Fuel definition	594 (69%)	190 (63%)	27 (100%)	6 (100%)	301 (74%)	18 (100%)	52 (98%)	—
Energy storage
Weight	92 (11%)	35 (12%)	6 (22%)	0 (0%)	37 (9%)	2 (11%)	12 (23%)	—
Volume	113 (13%)	15 (15%)	4 (15%)	0 (0%)	93 (93%)	0 (0%)	1 (2%)	—
Main battery specifications
Energy ($\mathrm{W}$$\mathrm{h}$)	19 (2%)	17 (6%)	—	—	—	2 (11%)	—	—
Capacity (mA)	61 (7%)	60 (20%)	—	—	—	1 (6%)	—	—
Voltage ($\mathrm{V}$)	48 (6%)	47 (16%)	—	—	—	1 (6%)	—	—

. This is a subset considering only fixed-wing UAVs, with or without Vertical Take-Off and Landing (VTOL) capability, with a take-off mass above one kilogram and encompassing the metrics relevant to the objectives of this work. Similar to the approach by Verstraete et al. [1], the classification of UAVs is based on the powertrain: internal combustion, fuel cell, battery electric, turbine, and solar. Building on their approach, the turbine category is subcategorized, and an additional group, generator, is also created.

Internal combustion UAVs comprise reciprocating and rotary internal combustion engines, while the turbine group includes turbojet, turboprop, and turbofan implementations. The differentiation of the generator implementations is based on the hybrid characteristics of such systems, which would enable them to benefit from the higher electrical efficiency and versatility in powertrain installation and from the comparatively high energy density of consumable fuels. Solar UAVs encompass all UAVs that have solar cells added, regardless of the size of the battery; hence, there are occurrences in which the solar supply is a limited boost to the battery capacity rather than the main supply.

The classification of VTOL UAVs is based on the horizontal propulsion system, either internal combustion or electric, depending on which provides the horizontal thrust. The use of the hybrid VTOL configuration combines the flexibility of the electrical powertrain in deployment and retrieval with the long endurance of the combustion implementation.

Moreover, the categorization used requires the definition of the propulsion system and, to distinguish between configurations, the specific fuel or energy carrier. For example, there are different implications for a hydrogen or methanol fuel cell and for a nickel–metal hydride or a lithium-ion battery. The available data on energy storage weights and volumes were recorded along with the available battery specifications.

Fitting a linearized power law to the estimated range from Equation (1) as a function of mass and fuel mass using bisquare weighting provides the results in

Table 1. Range scaling coefficients for the regressions $L=\alpha m^{\beta }$ and $L=\alpha m_{\mathrm{fuel}}^{\beta }$, with L in $\mathrm{k}\mathrm{m}$.

Classification	m [kg]										mfuel [kg]
	Count	$\mathit{\alpha }$	$\mathit{\beta }$	${\mathit{R}}^{\mathbf{2}}$	Domain of $\mathit{m}$						Count	$\mathit{\alpha }$	$\mathit{\beta }$	${\mathit{R}}^{\mathbf{2}}$	Domain of ${\mathit{m}}_{\mathbf{f}}$
All 1	503	46.01	0.63	0.74	[	1.1	:	14628	]		158	142.95	0.56	0.76	[	0.06	:	6577	]
Battery electric 2	193	50.47	0.43	0.25	[	1.1	:	55	]		43	103.37	0.42	0.61	[	0.42	:	13.8	]
Battery electric (all)	195	53.22	0.40	0.25	[	1.1	:	635	]		45	104.52	0.40	0.57	[	0.42	:	227	]
Internal combustion	260	141.27	0.45	0.47	[	2.5	:	5080	]		98	262.74	0.44	0.63	[	0.82	:	1980	]
Fuel cell	10	344.25	0.17	0.50	[	5	:	45	]		6	1201.50	0.36	0.32	[	0.06	:	0.63	]
Generator	2	119.06	0.25	—	[	45.4	:	208	]		0	—	—	—	—
Solar	7	28.88	1.23	0.42	[	4	:	19.3	]		2	173.02	0.03	—	[	0.83	:	3.6	]
Turbine	20	12.33	0.78	0.94	[	23	:	14628	]		7	414.26	0.42	0.82	[	300	:	6577	]
Turbofan	5	31.55	0.67	0.27	[	8255	:	14628	]		3	4.13	0.98	0.97	[	3583	:	6577	]
Turbojet	8	17.53	0.66	0.81	[	23	:	7500	]		0	—	—	—	—
Turboprop	7	83.89	0.55	0.72	[	1000	:	6146	]		4	866.19	0.32	0.63	[	300	:	1814	]

Coefficient $\alpha$ in $\mathrm{km}·{\mathrm{kg}}^{-\beta }$; $\beta$ is dimensionless. ¹ Includes UAVs with unknown powertrains. ² Two large UAVs were removed from the results and domain, as they were not well represented by the fit. See the text for details.

, along with a range of validity. Unless otherwise noted, all fitting operations consider bisquare weighting and log-linearization.

There is a significant difference in the number of entries per classification, resulting in varying confidence levels for the representativeness of the dataset for each specific analysis and powertrain. Therefore, the confidence in the representativeness is higher for the battery-electric and internal combustion implementations, and this is valid for the rest of this work. However, it is also relevant to note the differences in the domain of applicability.

There is a significant difference in the coefficient of determination $\left(R^2\right)$ value between battery-electric and internal combustion UAVs for the fit of range as a function of mass, which could be due, in part, to the more compact domains for mass and range. However, comparing the reduction in the $R^2$ of these two powertrains from fuel mass to total mass, the more significant reduction in $R^2$ for battery-electric UAVs suggests a higher variability among implementations compared to internal combustion UAVs. This occurs despite some battery-electric UAVs achieving ranges comparable to those of internal combustion UAVs (seen later in Figure 2b). These two powertrains are also the closest in terms of the general effectiveness of scaling as a function of either of these masses (coefficient $\beta$), which exhibits a consistent difference (0.02) between powertrains. Even though the battery-electric powertrain would be more energy-efficient, the lower coefficient $\beta$ suggests differences in the effectiveness of energy storage, which partially offsets the increased powertrain efficiency.

The results presented had two large battery-electric UAVs removed because their masses were tenfold those of the remaining data, making them unrepresentative in terms of the applicability domain; moreover, the resulting fit ($\alpha =53.2$ and $\beta =0.40$) overestimated the range of these battery-electric UAVs by at least 120%. This discrepancy motivated the exclusion of these two large UAVs from the specific analysis, since only these were between 55 kg and 600 kg. However, the addition of newly developed UAVs with masses between these values will increase representativeness in this region and may indeed lower the coefficient $\beta$.

Due to the limited data for fuel cell, solar, and generator implementations, generalizations are more uncertain. It is reasonable for solar UAVs to benefit more from increasing the overall mass than from increasing the battery size, because the increase in mass is associated with an increase in wingspan, as well as aerodynamic efficiency (see [11]), and thus the available area for photovoltaic panels. The impact of these differences results in a much higher scaling coefficient. Fuel cell UAVs would benefit more from an increase in fuel mass. This is due to the high energy density of hydrogen, as the ones in this subset used hydrogen fuel cells. Their reliance on the vehicle’s mass to achieve range is reduced when compared to the alternatives, as shown by the low exponent. An opposite trend is visible across the equivalent exponents for the solar and fuel cell implementations. Although they could be seen as complementary in theory, in practice, it is dubious under which circumstances this combination would be better than batteries or supercapacitors because of the in-flight recharging capability. Generator implementations are very scarce, with the upcoming implementations lacking credible or real-world data. From a theoretical point of view, these may eventually be found to be promising, although likely at larger UAV sizes to mitigate the additional weight of the powertrain and electrical buffer storage, which can cause difficulties for implementation at smaller UAV sizes.

The analysis of the turbine aggregate data shows high scaling values and fit fidelity. For the subcategorizations, there are preliminary data for the turbofans that evidence some of the largest exponents. Considering the size of these implementations, one can reason these large exponents to be in accordance with the effectiveness of the even larger airplane implementations, even more so, as some variants of the same base turbine are also installed in small airplanes. In fact, our turbofan airplane data point to exponents of 0.63 for mass scaling and 1.24 for fuel mass scaling. Note that, in addition to size differences, these airplanes will be using at least two turbofans instead of one. Turboprop base variants are also shared between large UAVs and airplanes but underperform compared to turbofans, thus replicating the pattern seen in airplanes. Compared to the non-turbine implementations, turboprops scale more effectively in terms of mass, but their scaling in terms of fuel mass does not distinguish them positively from the remaining powertrains. Scaling results for turbojet UAVs evidence a large exponent compared to the remaining configurations and cover the broadest range of masses in the turbine subcategory. However, no fuel mass data were found to assess the equivalent fit.

Range and Motion Diagram

The estimated values of the range, along with the speed data from the dataset, allow the inclusion of the UAV dataset in two literature plots. The first relates the range to their mass (Figure 2b), and the second relates the speed to their mass (Figure 2d,f), (see [3]). In these and subsequent figures, each shaded area defines the convex hull of a given UAV implementation. To enable a comprehensive view of the entire distribution of values, all histogram data are represented using equal-width bins, created by converting the data through the common logarithm, and will refer only to UAVs. The bands between the scatter plots and histograms (inter-plots) are projections of the airplane data in these scatters. The red bands show the values for Airbus’s and Boeing’s turbofan airplanes, and the blue bands show the equivalent for the turboprops. These bands correspond to the maximum fuel mass configuration, which is also plotted in the scatter plots, e.g., Figure 2b. The lightly shaded bands represent the airplane configuration prioritizing the payload over fuel mass. For each of the airplane configurations, (a) maximum payload at reduced fuel and (b) maximum fuel at reduced payload, an illustrative fit is plotted. These configurations are then connected with a shaded area demonstrating that, as mass increases, the difference between the configurations decreases. Note that the number of items in each plot will not always match, as not every entity has the same number of parameters available. Moreover, the maximum cruise speed of airplanes is mostly not provided by primary sources and thus not plotted.

Figure 2. Plots of range, cruise, maximum speed, and take-off mass. (a) A histogram of calculated UAV ranges and a scatter plot of these values with the ranges of airplanes in (b). (c) A histogram of UAV cruise speeds and a scatter plot of these values with the cruise speeds of airplanes in (d). (e) A histogram and scatter plot of UAV maximum speeds and a scatter plot of these values in (f). (g) A histogram of UAVs’ maximum take-off masses. Histogram data are presented using equal-width bins created by applying the common logarithm to the data. The bands between histograms and scatter plots are projections of the airplane values. In red are Airbus and Boeing turbofan airplanes and in blue are turboprop airplanes. The darker tone indicates the maximum fuel mass configuration, and the lighter tone indicates the maximum payload configuration.

Figure 2. Plots of range, cruise, maximum speed, and take-off mass. (a) A histogram of calculated UAV ranges and a scatter plot of these values with the ranges of airplanes in (b). (c) A histogram of UAV cruise speeds and a scatter plot of these values with the cruise speeds of airplanes in (d). (e) A histogram and scatter plot of UAV maximum speeds and a scatter plot of these values in (f). (g) A histogram of UAVs’ maximum take-off masses. Histogram data are presented using equal-width bins created by applying the common logarithm to the data. The bands between histograms and scatter plots are projections of the airplane values. In red are Airbus and Boeing turbofan airplanes and in blue are turboprop airplanes. The darker tone indicates the maximum fuel mass configuration, and the lighter tone indicates the maximum payload configuration.

The range of each airplane configuration was obtained from the payload–range diagrams, which would sometimes include a Mach value for airspeed, and either the altitude or the flight conditions assumed; these were converted into derived SI units using the following real-world-based expression:

$$u\left[\mathrm{k}\mathrm{m} {\mathrm{h}}^{-1}\right]=\left\{\begin{array}{cc}3.6\left(340.29-3.3865\times {10}^{-13}{a}^3-2.0987\times {10}^{-8}{a}^2-3.8394\times {10}^{-3}a\right)Ma,\hfill & \mathrm{if}a⩽11000,\hfill \\ 3.6\times 295.1,\hfill & \mathrm{if}11000<a⩽20100,\hfill \end{array}\right.$$

(2)

where a is the altitude in meters, and $Ma$ is the Mach value. This expression was computed by us based on the International Standard Atmosphere data for the speed of sound as a function of altitude [12], which is the basis for the payload–range diagrams used. The speed of sound decreases within the relevant range of flight altitudes, namely, up to 11 $\mathrm{k}$$\mathrm{m}$, and remains constant thereafter until 20 $\mathrm{k}$$\mathrm{m}$. This reduces the number of turbofan data points to 59 airplanes, but the illustrative fit is still plotted across the initial range of take-off masses. The same process is also applied to the turboprop dataset.

Figure 2a,b shows that UAVs are competitive with airplanes in terms of range. Turbofan, turboprop, and a considerable number of internal combustion UAVs achieve values of range comparable to those of the largest airplanes (turbofans). Notably, a significant proportion of the internal combustion UAVs match or even exceed the values of turboprop airplanes, particularly the ones with reduced speed (Figure 2b,d,f). One can postulate that the difference in range between internal combustion UAVs and turboprop airplanes is highly likely due to the reduction in energy expenditure (drag, D) resulting from the implied reduced wet area and the reduced speed (as D ∝ $u_{\mathrm{c}}^2$). The latter can be inferred by comparing their speed and mass, which, for UAVs, is half or less (Figure 2c,d). The reduced-wet-area argument is reinforced by examining the turbofan and turboprop UAVs, as both exhibit comparable maximum take-off masses to those of the turboprop airplanes but achieve significantly greater ranges, in turn, similar to the bigger airplanes (Figure 2b), while having similar speeds to turboprop airplanes (Figure 2c,d).

Turbine implementations provide varied results, and, while turbojets lead in speed, this inherent inefficiency severely reduces the achievable range compared to internal combustion implementations of similar size, as seen at the left edge of the turbine area in Figure 2b,d. As turbojet sizes increase and reach values similar to those of the turbofan and turboprop UAVs, the negative impact of scale decreases, and turbojet UAVs achieve ranges comparable to those of other turbine implementations of similar size. In contrast, most turboprop and turbofan configurations show reduced speeds compared to turbojets. In the case of some turboprops, this reduction makes their speed comparable to internal combustion implementations in some cases. It is unclear how a turboprop or turbofan would perform at lower take-off masses because of technical and economic limitations, which places them at a disadvantage compared to internal combustion.

Bejan’s theory regarding body size and adequate organ size (see [3]) argues for the existence of an optimal proportion between body and organ sizes, balancing the increased irreversibilities of smaller sizes and the weight inefficiencies of larger sizes. In this context, organ size corresponds (separately) to propulsion and to energy systems. In Figure 2b, the two largest battery implementations have range values that deviate significantly from the expected pattern of increasing with take-off mass, despite having congruent proportions of battery to take-off masses (14% and 34%). Application requirements could be a limiting factor, as other instances had higher proportions. Moreover, the local trend around 45 $\mathrm{k}$$\mathrm{g}$ appears to diverge from the global scaling after a peak at 20 $\mathrm{k}$$\mathrm{g}$. Considering this, until additional large battery-electric UAVs, preferably ones with larger proportions of battery mass, are developed, it is uncertain how the scaling of range will behave beyond the 45 $\mathrm{k}$$\mathrm{g}$ threshold, given that larger vehicles imply additional energy requirements. Furthermore, Stolaroff et al. [13] postulated a tendency toward a range threshold as the battery mass in a rotary-wing UAV increases.

However, in the context of a small UAV, it is also reasonable to assume that the addition of small amounts of fuel mass, in this case, batteries, has similar effects on the range because the negative scaling effects have not begun to manifest. These effects would only become more pronounced as the size and demands on the UAV increase. This can be an additional explanation as to why small UAVs are mostly electric: at their scale, the convenience and simplicity of the battery-electric powertrain make scaling penalties in weight a non-issue.

Although the cruise speeds of turbofan UAVs are more similar to those of turboprop airplanes, turboprop UAVs bridge the speed gap between turbofan UAVs and internal combustion UAVs, as shown in Figure 2b,d. This can be understood as a natural outcome of the fundamental mechanical implementation of turboprops and their inherent intermediate characteristics in terms of costs and technical requirements.

There is a reduced but evident overlap in the range between battery-electric and internal combustion implementations (Figure 2a,b), mostly occurring around the 30 $\mathrm{k}$$\mathrm{g}$ and 300 $\mathrm{k}$$\mathrm{m}$ cluster. The average range of internal combustion is approximately tenfold that of battery electric. The sporadic occurrence of internal combustion in the lower mass and range area may be attributed to battery-electric solutions providing a more compelling and versatile option, creating a market demand for them. Both battery-electric and fuel cell UAVs use electric engines, but fuel cell UAVs achieve longer ranges, which are typically only achievable at those masses by internal combustion implementations, as visible in Figure 2a,b.

Most electric UAVs have cruise speeds below 100 km h⁻¹, with an average of 65 km h⁻¹, but a few can reach above 200 km h⁻¹ maximum speed, which, in turn, averages 108 km h⁻¹ (Figure 2c,e). Fuel cell implementations exist within the battery-electric hull, given that the propulsion system is of the same type. Ultimately, the selection between energy storage media for the electric powertrain only has a more noticeable impact on range.

Internal combustion implementations share some of this design space, but their typical speeds match the upper bounds of the battery-electric cruise and maximum speeds, with averages of 118 km h⁻¹ and 182 km h⁻¹. The maximum and average speeds (cruise and maximum) for electric UAVs (battery electric and fuel cell) are almost halved when compared to internal combustion implementations (Figure 2c,e). While market forces and the small sizes of these UAVs have an impact, it is important to highlight the potential technical limitations on the electric motor and battery side. The power requirements scale with the cubic of the speed. Since the rotational speed of an electric motor is given by the current, higher rotational speeds require battery configurations capable of delivering larger currents, which will tend not to be as optimized for capacity in terms of mass.

Turbine implementations are located mostly in or beyond the upper bound of the internal combustion hull, supporting an argument for their selection based on this characteristic (Figure 2d). An analogous situation occurs in terms of maximum speed (Figure 2f). Therefore, it is clear that turbine implementations provide superior speed performance compared to the other implementations.

Focusing now on the mass distribution (Figure 2g), there is a clear distinction in the distributions of UAVs. Electrical UAVs are mostly below the 20 kg threshold, and the opposite occurs for internal combustion UAVs. The range of weights of fuel cell UAVs is also found within this electric group, and that of the ones using turbines are mostly included in the internal combustion group, extending it slightly toward higher values, even though turbine implementations tend to be lighter than internal combustion engines for the same power output.

Comparing the increase in cruise speed as a function of mass previously reported in the literature, Bejan’s result mostly focuses solely on biological flyers, underestimating the cruise speeds of human-made flyers [3], while Gurevich and Arav [2] bridge biological flyers and turbofan airplanes, which, as they suggest, overestimates UAV cruise speeds but, based on our data, underestimates turbojet UAVs. Our fit considering only UAVs would traverse the regions of higher data density (battery electric and internal combustion) but would be unable to adequately capture turbine-based implementations of any type, except for the smaller turboprops, with the remaining diverging from the fit. Therefore, while mass does influence speed, other parameters, including the propulsion system, seem more relevant, as also shown later in Table 2 by the reduced $\left(R^2\right)$. In terms of powertrain, battery-electric UAVs show more stable values than internal combustion implementations, as thermal implementations are more sensitive to scaling than electric motors. Turbine implementations show a band of increase, tending toward airplane-size performance.

Although Figure 2c,d indicates a slight increase in turbofan aircraft speed with mass, this may in fact be caused by aerodynamic features that have allowed the aircraft to operate in the transonic regime (supercritical airfoils, swept wings, etc.), as previously stated by Chernyshev et al. [14]. The data shown consider implementations from different years, even with retrofits, with different technology levels, which may attribute this perception of a speed increase solely to mass and not to technological development, even though there is a general correlation between technological development and take-off mass (see [3]).

Finally, the target applications of these vehicles also play a role. Combustible-fuel UAVs remain dominant in the military and security infrastructure, whereas electrical UAVs are more common among civilian users and for business applications. Therefore, their development motivations may differ, and thus, they prioritize different characteristics, such as payload; speed; acoustic, thermal, or radar signatures; endurance; among others.

Assessing the scaling of cruise speed based on mass yields the results in Table 2, which can be analyzed together with the dispersions in Figure 2d to reach a set of inferences. There is a general tendency for speed to increase with mass. Solar UAV implementations evidence higher scaling effectiveness than batteries, as the increase in mass benefits the aerodynamic efficiency through increases in the wingspan, lift-to-drag ratio, and aspect ratio, which could allow for less demanding speeds and power demands, reducing the impact of increasing the size of the battery and its weight. However, the strong increase in speed is due to the higher altitudes that these solutions tend to fly, which require higher speeds to offset the reduction in air density and generate enough lift. Generator implementations have a low coefficient between battery-electric and internal combustion UAVs, but the lack of data hinders further inferences. Fuel cell implementations see a significant increase in speed with mass. Due to the reduced number of implementations and the dispersion in mass, this could be attributed to the development and improvement of the underlying technologies over time.

Table 2. Cruise speed scaling coefficients for the regression $u_{\mathrm{c}}=\alpha m^{\beta }$, with $u_{\mathrm{c}}$ in km h⁻¹ and m in $\mathrm{k}\mathrm{g}$.

Classification	Count	$\mathit{\alpha }$	$\mathit{\beta }$	${\mathit{R}}^{\mathbf{2}}$	Domain of m
All 1	534	43.83	0.19	0.77	[	1.1	:	14628	]
Battery electric	205	49.03	0.12	0.36	[	1.1	:	635	]
Internal combustion	272	50.43	0.16	0.58	[	2.5	:	5080	]
Fuel cell	12	18.61	0.45	0.47	[	5	:	45	]
Generator	3	82.61	0.15	0.40	[	45.4	:	551	]
Solar	9	31.23	0.27	0.81	[	4	:	862	]
Turbine	23	126.23	0.16	0.27	[	23	:	14628	]
Turbofan	6	6084.8	−0.25	0.96	[	2722	:	14628	]
Turbojet	9	164.60	0.16	0.86	[	23	:	7500	]
Turboprop	8	1.30	0.67	0.74	[	1000	:	6146	]

Coefficient $\alpha$ in $\mathrm{km}·{\mathrm{s}}^{-1}·{\mathrm{kg}}^{-\beta }$; $\beta$ is dimensionless. ¹ Includes unknown powertrains.

Table 2. Cruise speed scaling coefficients for the regression $u_{\mathrm{c}}=\alpha m^{\beta }$, with $u_{\mathrm{c}}$ in km h⁻¹ and m in $\mathrm{k}\mathrm{g}$.

Classification	Count	$\mathit{\alpha }$	$\mathit{\beta }$	${\mathit{R}}^{\mathbf{2}}$	Domain of m
All 1	534	43.83	0.19	0.77	[	1.1	:	14628	]
Battery electric	205	49.03	0.12	0.36	[	1.1	:	635	]
Internal combustion	272	50.43	0.16	0.58	[	2.5	:	5080	]
Fuel cell	12	18.61	0.45	0.47	[	5	:	45	]
Generator	3	82.61	0.15	0.40	[	45.4	:	551	]
Solar	9	31.23	0.27	0.81	[	4	:	862	]
Turbine	23	126.23	0.16	0.27	[	23	:	14628	]
Turbofan	6	6084.8	−0.25	0.96	[	2722	:	14628	]
Turbojet	9	164.60	0.16	0.86	[	23	:	7500	]
Turboprop	8	1.30	0.67	0.74	[	1000	:	6146	]

Coefficient $\alpha$ in $\mathrm{km}·{\mathrm{s}}^{-1}·{\mathrm{kg}}^{-\beta }$; $\beta$ is dimensionless. ¹ Includes unknown powertrains.

Internal combustion UAVs show an increase in speed with mass, which ranges across three orders of magnitude, with battery-electric UAVs evidencing a slower increase. Scale factors can also be a reason, as electric motors are less affected by inefficiencies at small scales compared to thermal engines. In fact, this is partially seen in Figure 2d, as several battery-electric UAVs present significantly higher speeds compared to their general cluster. Notwithstanding this, market forces could again be influencing such implementations.

As a category, turbine implementations show weak speed scaling with mass. Notably, turbojets exhibit reduced scaling, potentially due to structural or aerodynamic limitations inherent to their high speed in relation to their mass. Conversely, turboprops show strong scaling, and as shown in Figure 2b,d, it is the speed that distinguishes these implementations from internal combustion, not the achievable range. Turbofans show a negative exponent due to the limited data and newer models’ change in design purpose from surveillance, monitoring, and ground attack to air combat. These require higher speeds that tend toward the transonic flight domain, as perceivable from the maximal speed plot, Figure 2f, and the airplanes in the cruise speed plot, Figure 2d.

The proportions of different UAV speeds did not evidence any scaling pattern with mass; instead, they tended toward different values, with the occasional outlier, and varied among the different powertrains. The ratios between cruise and maximum speeds tend to values of 0.59, 0.63, and 0.75 for battery-electric, internal combustion, and turbine implementations. The equivalent ratios for loitering tend to 0.44 and 0.49 for the battery-electric and internal combustion implementations and 0.44 and 0.42, respectively, for the stall-to-maximum-speed ratio. For brevity, these distributions are not presented.

The assumption linking mass and speed is generally more coherent with fossil fuel propulsion systems. From Figure 2c–f, electrically driven UAVs can achieve higher speeds with lower take-off masses, particularly cruise speeds.

3. Transportation Efficiency

3.1. Payload Diagrams

Two additional metrics are useful in assessing platforms. The first considers the maximum transport work, resulting from the product of the payload and range (Figure 3a,b), while the second considers what can be defined as loitering or surveying work, in turn resulting from the product of the payload and endurance (Figure 3c,d). Transport work is more relevant for logistics and supply activities and surveying work for time-sensitive applications such as surveying, monitoring, and surveillance. Due to Equation (1), these two metrics are related to each other through the speed,

$$Payload·Range=Payload·Endurance·CruiseSpeed.$$

(3)

For the assessment of surveying work (Figure 3c,d), the flight duration of the airplanes is estimated based on the time required to traverse the given range at the cruise speed provided in the manufacturers’ diagrams.

Both the transport and surveying work of UAVs can reach values similar to those of airplanes (Figure 3a,c). Although there is still a difference compared to the larger airplanes in terms of transport work (Figure 3b), this difference is substantially reduced when the impact of speed is removed (surveying work) (Figure 3d). In this surveying work, it is also possible to see a significant increase in the amplitude of the UAV data, which contrasts with the more compact distribution of the transport work (Figure 3b). Part of the similarity in the general pattern of the distributions occurs because the range is a function of cruise speed and endurance. For the same available energy, an increase in speed or payload mass increases energy expenditure, which reduces range and endurance. In the case of airplanes, this trade-off is visible as a shaded area of small amplitude, indicating a low variation in these metrics for the different configurations, provided that the take-off mass is maximized (Figure 3b,d).

Battery-electric UAVs exhibit these two characteristics with values very similar to those achievable with internal combustion UAVs up to 15 $\mathrm{k}$$\mathrm{g}$, also shown by the overlapping clusters and hulls in Figure 3c,d. As the take-off mass increases beyond 15 $\mathrm{k}$$\mathrm{g}$ and until 50 $\mathrm{k}$$\mathrm{g}$, the values are still similar, but the difference in the distribution between the two becomes increasingly more noticeable. Toward smaller masses, the design space is dominated by battery-electric UAVs, which perform as well as, or better than, the reduced number of internal combustion UAVs.

Figure 3. Plots of maximum payload metrics. (a) A histogram of maximum payload × range for UAVs and a scatter plot of the same with turboprop airplanes and Airbus and Boeing’s airplanes in (b). (c) A histogram of maximum payload × endurance for UAVs and a scatter plot of the same with turboprop airplanes and Airbus and Boeing’s airplanes in (d). The bands between histograms and scatter plots are projections of the airplane values. In red are Airbus and Boeing turbofan airplanes and in blue are turboprop airplanes. The darker tone indicates the maximum fuel mass configuration, and the lighter tone indicates the maximum payload configuration.

Figure 3. Plots of maximum payload metrics. (a) A histogram of maximum payload × range for UAVs and a scatter plot of the same with turboprop airplanes and Airbus and Boeing’s airplanes in (b). (c) A histogram of maximum payload × endurance for UAVs and a scatter plot of the same with turboprop airplanes and Airbus and Boeing’s airplanes in (d). The bands between histograms and scatter plots are projections of the airplane values. In red are Airbus and Boeing turbofan airplanes and in blue are turboprop airplanes. The darker tone indicates the maximum fuel mass configuration, and the lighter tone indicates the maximum payload configuration.

The previous statement on the opposing effect of speed on the range is further validated when remembering Figure 2d and the comparatively low speeds of solar and fuel cell UAVs. Although of a limited number, these implementations evidence comparable results to the internal combustion implementations (Figure 3b,d) if omitting payload considerations. Fuel cell UAVs appear again at the interface between battery-electric and internal combustion hulls.

Although there is only a limited number of solar UAVs, we could identify two different types of configurations. The first focuses on achieving high endurance even at a significant cost in payload and speed, as wing loading and aerodynamic efficiency are critical (see [11,15]). An example like this can be seen near the fuel cell cluster $(m\approx 15 \mathrm{k}\mathrm{g})$ in Figure 2b,d and Figure 3d. The second configuration consists of conventional battery-electric UAVs with solar cells as an add-on. These increase the energy available for motion or for the payload (see [16]).

The development of transportation and surveying UAVs becomes more relevant and credible as both metrics show very high values, at times comparable to airplanes. However, justifying this statement across transportation systems requires a further comparison to effectively contextualize them against existing systems.

3.2. Transportation Metrics

Although both transport and surveying work have merit, there are other metrics commonly used to assess transportation systems and their efficiency. These are classified as transportation statistical and efficiency metrics and include Vehicle Kilometers (VKMs), Tonne Kilometers (TKMs), energy intensity (EI), and energy per kilometer (EK). VKMs signify the total number of kilometers traveled by a set of vehicles ($\mathrm{k}\mathrm{m}$), TKMs the product of the payload and the distance it was transported (t · km), EI the energy consumed to transport a tonne of cargo for one kilometer, and EK the energy consumed to move one kilometer. By definition, VKMs and TKMs rely on real use data, use that may be off-design and thus cannot be assessed. However, theoretical data can be inferred for the EI and EK. These specific metrics provide insights across different transportation systems, specifically the impacts of adding more payload or covering longer distances, and are usually presented as a function of the average payload or occupancy. The values presented will be based on the energy entering the system before any efficiency penalty and without any consideration of the production, refining, transmission, and storage of the energy or energy carrier.

For fuel cells and all thermal engines, the available energy is given by the mass of the fuel and its heating value. This mass of fuel was either stated directly or obtained through the fuel capacity for which the specific fuel was known. Hydrogen fuel cell UAVs had the fuel weight provided or calculated through pressure, density, and volume. For battery-electric implementations, the available energy was provided directly by the manufacturer as battery energy (Wh) or calculated through the battery capacity (mAh) and its voltage ($\mathrm{V}$), which was either specified directly or derived from the arrangement of the battery cells. It is worth noting that the availability of manufacturer data for these elements is scarce, which reduces this subset to a total of 209 implementations, categorized into 66 battery-electric, 121 internal combustion, 3 solar-battery, 6 fuel cell, and 13 turbine implementations. The 13 turbine implementations are further divided into 4 turbofans, 2 turbojets, and 7 turboprops.

In Figure 4, four graphs are presented, with the top row demonstrating the energy per kilometer (Figure 4a) and energy per hour (Figure 4b) and the bottom row with the conventional energy intensity per kilometer (EI) (Figure 4c) and the equivalent considering endurance instead of range, energy intensity per hour (EIH) (Figure 4d), thus maintaining consistency with the metrics previously used. Here, the payload is a proxy for TKM, as reasoned in Equation (4), under the assumption that the UAV is conducting a survey mission rather than a drop-off or delivery. In the latter case, the equivalent EI could double and TKM halve as the vehicle traverses the same distance but carries the payload only in the first half. The actual energy intensity in this scenario depends on other specifics of the UAV implementation and operational parameters, such as the powertrain, flight speed, and fuel loading (if consumable), among other factors.

$$\begin{array}{cc}\hfill {\displaystyle \frac{TKM}{VKM}}& ={\displaystyle \frac{Payload\times Distancewithpayload}{Totaldistancecovered}}\hfill \\ \hfill & \Rightarrow \left\{\begin{array}{cc}\phantom{{\displaystyle \frac{1}{2}}}Payload\hfill & \mathrm{if}distancewithpayload=\phantom{{\displaystyle \frac{1}{2}}}totaldistancecovered,\hfill \\ {\displaystyle \frac{1}{2}}Payload\hfill & \mathrm{if}distancewithpayload={\displaystyle \frac{1}{2}}totaldistancecovered.\hfill \\ \phantom{{\displaystyle \frac{1}{2}}}\dots \hfill \end{array}\right.\hfill \end{array}$$

(4)

In Figure 4a, there are minor overlaps among all powertrains, despite significant differences in achievable ranges and endurances. As in previous cases, the hydrogen fuel cell UAVs bridge the gap between internal combustion and battery electric. The turboprop and turbofan implementations exhibit characteristics similar to those of internal combustion, without significantly differentiating themselves in this metric. Due to the lack of turbojet data, no conclusions can be drawn on them.

Figure 4. Plots of UAV energy intensity and energy consumed per kilometer and per hour as functions of payload: (a) energy per kilometer, (b) energy per hour, (c) energy intensity per kilometer, and (d) energy intensity per hour. The fit on truck data is denoted by $\Delta$, based on [5], while theoretical airplane data are denoted by $\delta$. For the fits in (a) and (b), a more horizontal slope implies better performance when increasing the payload, while for the fits in (c) and d), a more vertical slope has the equivalent interpretation; see the corner of each panel for a quick reference.

Figure 4. Plots of UAV energy intensity and energy consumed per kilometer and per hour as functions of payload: (a) energy per kilometer, (b) energy per hour, (c) energy intensity per kilometer, and (d) energy intensity per hour. The fit on truck data is denoted by $\Delta$, based on [5], while theoretical airplane data are denoted by $\delta$. For the fits in (a) and (b), a more horizontal slope implies better performance when increasing the payload, while for the fits in (c) and d), a more vertical slope has the equivalent interpretation; see the corner of each panel for a quick reference.

Another aspect comes from the right edge of the hull, as the indicative data for large battery-electric UAVs tend toward some large internal combustion UAVs. Despite the comparable energy and payload, the ranges of these two vehicles were much lower than most of the internal combustion implementations, as seen in Figure 2b. Due to the gap in the values of payload, only battery-electric UAVs with up to 4 $\mathrm{k}$$\mathrm{g}$ of payload can confidently be generalized as more energy-efficient than internal combustion, even though the range can differ significantly.

When considering the energy per hour in Figure 4b, there is a clear resemblance to the energy per kilometer in Figure 4a. Notwithstanding this, we see a minor increase in dispersion in all groups. In this case, battery-electric UAVs with payloads up to 10 $\mathrm{k}$$\mathrm{g}$ can be generalized as more energy-efficient per flight hour compared to the remaining implementations.

In Figure 4c, additional lines are included to represent the theoretical $1:1$ decreasing ratio, similar to what Schäfer and Yeh [17] traced for different transportation systems. Consistent with their reasoning, the fits for the different UAV populations reveal a misalignment with this $1:1$ ratio, demonstrating the increased energy expenditure associated with increasing the payload of the vehicle. However, it also evidences the inherent economies of scale in transportation, with a more horizontal fit demonstrating worse benefits. A clear downward trend is observed for all UAV classifications, even though confidence in the slope varies. Based on the current data, the steepest slope is exhibited by fuel cell UAVs, followed by battery electric, turbine, and internal combustion. However, the confidence in the fuel cell and turbine results is lower due to the reduced number of entries. The two large-payload battery-electric UAVs are excluded from this assessment as outliers, but the fits with them are drawn dotted.

Nevertheless, more empirical data on how this metric evolves is necessary to assert the behavior when comparing UAVs with other transportation systems. To address this, we rely on the work by Gucwa and Schäfer [5], who obtained and compared the real-world energy intensities of trucks, trains, airplanes, and ships. We then estimated the theoretical energy intensity of airplanes based on our data, denoted by the Greek letter $\delta$ in Figure 4c, and observed it to be consistent with their results. Additionally, a regression was calculated based on their truck energy intensity data, yielding the plot denoted by the Greek letter $\Delta$. Notably, a cluster of their truck data overlapped our turbine hull, specifically between around 150 $\mathrm{k}$$\mathrm{g}$ and 300 $\mathrm{k}$$\mathrm{g}$ of payload. Their data were distributed between this lower limit and around 20000 kg. Train and ship data were omitted because efficiency and economies of scale place them below the $1\times {10}^{-3}$ $\mathrm{M}$$\mathrm{J}$ ${\mathrm{kg}}_{\mathrm{payload}}^{-1}$ threshold. Note that there are lower payload limits to truck and airplane data, and beyond these limits, the plots are depicted with dashed lines.

As the payload size increases, the differences in energy intensity between UAVs and the remaining transportation systems decrease until exceeding that of trucks (Figure 4c). For large payloads, current UAVs are at least comparable to trucks while being unaffected by geographical or traffic limitations. For smaller payloads, battery-electric UAVs, particularly VTOL, seem a viable option, which is in accordance with developments in both academia and industry, even though they focus more on rotary-wing implementations [18,19,20,21]. Nevertheless, these smaller UAVs need to be compared to smaller vehicles, including e-bikes, similarly to the rotary-wing UAVs in [22]. Non-VTOL fixed-wing UAVs have higher values of range and speed but additional take-off and landing requirements, making them distinct from the commonly studied rotary-wing and VTOL fixed-wing UAVs; see [20,21,22].

Aerial locomotion is inherently more energy-intensive than the terrestrial equivalent, and, in Figure 4c, airplanes are roughly one order of magnitude more energy-intensive than trucks. This leads to the question of whether Unmanned Ground Vehicles (UGVs) will demonstrate a similar reduction in energy intensity compared to UAVs and how their characteristics and constraints related to the application will affect this comparison. Moreover, as UGVs have greater payload capacities and lower speeds and ranges [18], this suggests a reduction in energy intensities.

The energy intensity per hour in Figure 4d shows a similar pattern to the energy intensity in Figure 4c, with the dispersion also increasing. Even considering the reduced number of entries and lower confidence, the steepest slope is exhibited by fuel cell UAVs, followed by turbines, battery electric, and internal combustion. Excluding the influence of the large battery-electric UAVs, we see a clear distinction between battery-electric and combustion powertrains; specifically, both energy intensity metrics of battery-electric implementations are lower than those of internal combustion for comparable payload values.

4. Fuel, Energy, and Powertrain

The improvement of UAV powertrains poses challenges when estimating UAV characteristics based on take-off mass fits. Although the different powertrains have similar proportions of vehicle mass allocated to energy storage, the associated energies are very different. Both challenges can be overcome by shifting the analysis from mass to the useful energy of the system, W, which can be obtained through the overall efficiency, ${\eta }_{\mathrm{o}}$, and the total energy of the system, E:

$$W={\eta }_{\mathrm{o}}E={\eta }_{\mathrm{c}}{\eta }_{\mathrm{tr}}{\eta }_{\mathrm{p}}E.$$

(5)

Due to practical considerations, we will dispense with the transmission efficiency, ${\eta }_{\mathrm{tr}}$, and focus on the more significant conversion and propulsive efficiencies, ${\eta }_{\mathrm{c}}$ and ${\eta }_{\mathrm{p}}$, respectively. The conversion efficiency is equivalent to the thermal efficiency or discharge and electrical efficiency depending on the powertrain.

In the absence of specific data and considering the objective of this analysis, representative values will be used for these efficiencies. A broad factor of 0.33(3) is considered as the thermal efficiency for turbine implementations and 0.25 for internal combustion. The conversion efficiency of fuel cells is given by a factor of 0.5, while battery-electric and solar implementations have a factor of 0.90 for battery discharge. These three powertrains are further adjusted by an additional factor of 0.90 to account for the electric motor efficiency. A propulsive factor of 0.80 is considered for all implementations. Due to the reduced speed of the turbojet implementation in this subset, a further halving of the propulsive efficiency is considered.

Recalling the introductory thesis on the conforming effects of the environment on air vehicles, if considering the energy per kilometer and per hour as functions of the useful energy, a collapse of the data occurs, as shown in Figure 5a,b. This aligns the different powertrains according to the demands of the environment, with the general pattern described by the function in black. The dispersion can in part be attributed to the different characteristics of the implementations, for example, speed or payload.

The UAV characteristics discussed previously are now shown in Figure 6 as a function of the calculated useful energy. In the case of maximum take-off mass and range, fits are displayed for the different powertrains using all available data. However, for the remaining characteristics, only battery-electric and internal combustion powertrains have their fits plotted. The remaining powertrains have limited data and increased dispersions, which reduces confidence in the representativeness of their fits. Moreover, the two large battery-electric UAVs are excluded from the fits for these remaining characteristics to ensure consistent comparisons, as their inclusion would cause deviations. These are plotted dotted and for illustrative purposes only. Before discussing each subfigure, a global pattern is clear: we observe a positive monotonic correlation between the useful energy and each characteristic, which shows an increase with useful energy by powertrain configuration from battery-electric to fuel cell and subsequently to internal combustion and turbine configurations.

The maximum take-off mass scales very closely with the useful energy across the thermal solutions in Figure 6a, scaling the slowest for battery-electric implementations. This means that battery-electric UAVs require comparatively more useful energy to be added to increase in size. This seems to be influenced by the useful energy density, where the lower the value, the steeper the slope. Fuel cell UAVs are positioned between battery-electric and internal combustion, implying intermediate useful energy densities. Internal combustion UAVs exhibit the broadest range of useful energies. Turbine-based UAVs appear in the upper part of the internal combustion hull and have the highest values of mass and useful energy. The general pattern suggests stronger scaling dynamics for turbine and internal combustion and only then for fuel cell and battery-electric implementations.

Figure 6. UAV energy plots. The scaling of different metrics according to the useful energy carried by a UAV: (a) maximum take-off mass, (b) range, (c) endurance, (d) payload, (e) payload × endurance, (f) payload × range, (g) maximum speed, and (h) cruise speed.

Figure 6. UAV energy plots. The scaling of different metrics according to the useful energy carried by a UAV: (a) maximum take-off mass, (b) range, (c) endurance, (d) payload, (e) payload × endurance, (f) payload × range, (g) maximum speed, and (h) cruise speed.

As a corollary of the take-off mass, the range increases the fastest for battery-electric implementations (Figure 6b), and the previous slower increase in mass with the increase in useful energy manifests itself as an advantage in range, albeit for a limited scope. While turbine implementations begin to appear at the upper edge of internal combustion, fuel cell UAVs are almost isolated and achieve ranges that would require internal combustion UAVs to have more than a five-fold increase in total energy.

Endurance shows a large dispersion, an analogous pattern to the range (Figure 6b,c), as expected since $L=u_{\mathrm{C}}h$. The single turbojet sample is completely isolated from the other turbine implementations, possibly due to the influence of the high speed, as seen later in Figure 6g,h. While the endurance of internal combustion UAVs increases significantly with the useful energy, these require more of it to reach the upper bound of the endurance of hydrogen fuel cell UAVs.

This outcome can be partly attributed to their payload capacity, as seen in Figure 6d, for both fuel cell and battery-electric UAVs. Fuel cell UAVs have payload capacities that are in line with the expectation for battery-electric and small internal combustion UAVs but are low compared to UAVs of similar endurance. Larger proportions of payload capacity cause a decrease in endurance and range, which is exemplified by the battery-electric UAVs with higher payload capacities than fuel cell UAVs (Figure 6b–d).

Both payload-derived metrics, Figure 6e,f, shows compact dispersions with the useful energy carried. Battery-electric UAVs show a reduced improvement rate, whereas their internal combustion counterparts show a much higher rate. Both the dispersion and the increase rate replicate the general pattern seen in Figure 3b,d, with a more compact alignment across all powertrains. The high range and endurance of fuel cell UAVs are offset by their limited payload capacity, resulting in values for these payload-derived transport metrics in line with the scaling pattern of battery implementations.

Compared to the remaining implementations, for most battery-electric UAVs, the useful energy has a reduced impact on cruise speed and a negligible one in the case of the maximum speed (Figure 6g,h). For internal combustion, despite the significant dispersion, there is an increase in both speeds with useful energy, which is slightly stronger for the cruise speed. Turboprop implementations, however, show a clear and sharp pattern of increase in both cases. Although both turbofans and turbojets lack data, turbofans show very high speeds, potentially suggesting an aerodynamic speed limitation. According to the previously mentioned evolutionary argument of organ size and balanced body and organ sizes, this increase in performance would be explained by the increase in the size of the engine and, naturally, of the UAV in which it is installed: a pattern common to airplanes, as the total engine mass increases with the size of the airplane (see [3]). Furthermore, the thermal implementations benefit significantly more in efficiency when increasing the size of the powertrain compared to electric implementations.

A potential correlation may exist between the use of electric motors, the small size of battery-electric and fuel cell UAVs, and their comparatively low speeds, which may be attributable to the power delivery components themselves. The performance of both fuel cells and batteries scale in a quasilinear form due to the characteristics of the components involved. Therefore, a low speed reduces the power requirements of both and thus their weights. In the case of batteries, this gives more flexibility to the arrangement of the cells. It is also conceivable that fuel cell implementations have been targeting endurance and range (Figure 6b,c), partially through the use of lower cruise speeds compared to their battery-electric counterparts; see Figure 6h.

A logical analysis can be conducted on the relationship between the expected behavior of cruise and maximum speeds with the useful energy of the battery-electric UAVs. The motivation to increase useful energy would be to increase endurance. The primary way to increase speed is to increase the installed power. However, increasing this power would require adding weight to the powertrain or modifying the aerodynamic characteristics. Although increasing the maximum speed inherently has more drawbacks than increasing the cruise speed, the latter can be a compromise to increase lift due to increased mass, for example, of energy storage, at the cost of decreased energy efficiency from drag.

Table 3. Fits for range as a function of useful energy, $L=\alpha W^{\beta }$, with L in $\mathrm{k}\mathrm{m}$ and W in $\mathrm{M}\mathrm{J}$.

Classification	Count	$\mathit{\alpha }$	$\mathit{\beta }$	${\mathit{R}}^2$	Domain of W
All	153	131.10	0.41	0.85	[	0.24	:	74,923	]
Battery electric 1	39	133.18	0.49	0.69	[	0.24	:	5.41	]
Internal combustion	98	102.74	0.44	0.63	[	6.40	:	17,226	]
Fuel cell	6	314.16	0.36	0.32	[	2.68	:	27.47	]
Turbine	7	145.72	0.43	0.82	[	3445	:	74,922	]
Turbofan	3	0.38	0.98	0.97	[	40,816	:	74,923	]
Turboprop	4	396.08	0.32	0.63	[	3445	:	25,830	]

Coefficient $\alpha$ in $\mathrm{km}·{\mathrm{MJ}}^{-\beta }$; $\beta$ is dimensionless. ¹ Two large UAVs were removed from the results and domain, as they were not well represented by the fit. See the text regarding Table 1 for details.

presents the fits for range as a function of the useful energy content, which are seen in Figure 6b. Interpreting the regression results (in log-space) within the domain of validity of this subset, it is also possible to infer the following patterns. Battery-electric vehicles provide more range for reduced values of useful energy stored; this is interpreted from the large coefficient and factor. Internal combustion implementations have a lower exponent, but the domain of applicability is non-intersecting with the results of the main battery-electric cluster. Fuel cell implementations bridge the values of useful energy between battery electric and internal combustion, evidence a reduction in the scaling effects with useful energy compared to both, and provide more range within their domain. Solar UAVs were not possible to include as a category due to limited data on energy storage.

Turbofans and turboprops are implemented only at high useful energy levels, which can be explained by the costs and specific demands of the military market. Despite the very limited data, turbofans evidence the largest exponent, and turboprops the smallest. Turbines will tend to be more reliable and lighter than internal combustion engines for similar performance, allowing for additional payload, fuel, or weight savings, which can then contribute to offsetting the reduction in efficiency associated with the increased speed. Although there were turbojet implementations with lower masses that would not allow for the useful energy levels in Table 3, none of them had enough parameters available to be included in this analysis.

As seen in Figure 6a, there is an alignment of most implementations when differentiating between thermal and battery-based implementations. The take-off mass, which is commonly used by empirical expressions, is correlated very strongly with the useful energy:

$$m=\left\{\begin{array}{c}\begin{array}{ccc}5.363W^{0.616},\hfill & \mathrm{All},\hfill & R^2=0.902,\hfill \\ 1.223W^{0.838},\hfill & \mathrm{Thermal}\mathrm{and}\mathrm{Hydrogen},\hfill & R^2=0.954,\hfill \\ 7.351W^{0.734},\hfill & \mathrm{Battery}\mathrm{and}\mathrm{Solar},\hfill & R^2=0.890.\hfill \end{array}\hfill \end{array}\right.$$

(6)

This allows for the estimation of the UAV mass from its useful energy, or, if inverted,

$$W=\left\{\begin{array}{c}\begin{array}{ccc}0.121m^{1.481},\hfill & \mathrm{All},\hfill & R^2=0.900,\hfill \\ 1.019m^{1.144},\hfill & \mathrm{Thermal}\mathrm{and}\mathrm{Hydrogen},\hfill & R^2=0.955,\hfill \\ 0.127m^{1.072},\hfill & \mathrm{Battery}\mathrm{and}\mathrm{Solar},\hfill & R^2=0.854.\hfill \end{array}\hfill \end{array}\right.$$

(7)

This establishes an empirical relationship between the take-off mass and the useful energy that the vehicle is expected to carry. Additional work is required to assess the possibility of integrating this relationship as an auxiliary in the conceptual phase or, more iteratively, in the design phase of UAVs.

Moreover, by applying the previous reasoning to estimate the useful energy in airplanes, both turbofan and turboprop, albeit with a slightly higher efficiency value $\eta \approx 0.40$, thus in agreement with increases in scale and the turbofan bypass ratio (see [3]), it is possible to establish a parallel between airplanes and thermal UAVs:

$$\begin{array}{cc}m=1.888W^{0.824}\hfill & R^2=0.989,\hfill \end{array}$$

(8a)

$$\begin{array}{cc}W=0.728m^{1.176,}\hfill & R^2=0.987.\hfill \end{array}$$

(8b)

The similarity between the exponents of the UAV and airplane scaling is clear, despite the significant difference in the scales being considered.

Going one step forward and again remembering the introductory thesis that airplanes and UAVs should conform to the same constraints and demands, all of the data can be considered as a single dataset, $N=383$, resulting in

$$\begin{array}{cc}m=1.065W^{0.865},\hfill & R^2=0.996,\hfill \end{array}$$

(9a)

$$\begin{array}{cc}W=0.983m^{1.151},\hfill & R^2=0.997.\hfill \end{array}$$

(9b)

This relationship is illustrated in Figure 7 in red. The exclusion of battery-electric and solar UAVs was not found to significantly affect this linearized fit due, in part, to the now-reduced number of entries. Even though there is a deviation from the power law, the linearized fit result remains robust:

$$\begin{array}{cc}m=1.090W^{0.863},\hfill & R^2=0.996,\hfill \end{array}$$

(10a)

$$\begin{array}{ccc}\hfill & W=0.957m^{1.153},\hfill & R^2=0.996.\hfill \end{array}$$

(10b)

If directly fitting the data without log-linearization, the curve marginally changes in the UAV region:

$$m=1.976W^{0.819},R^2=1.\phantom{00..}$$

(11)

However, it is still unable to capture either the battery-electric or solar UAVs, which are only effectively described by Equation (6), illustrated in Figure 7 in green. Independently of the exclusion of the large battery-electric UAVs, we see significant proximity to or an intersection with turboprop airplanes, which are in fact the development target of battery-electric aircraft.

The linearized fit is found to be congruent with non-battery and non-solar UAVs, as well as airplanes. Although there seems to be a correlation between the congruence of the data with the fit and the vehicle’s mass decreasing during flight, this should not be regarded as the cause, as hydrogen-fuel cell UAVs do not evidence a significant decrease in vehicle weight as the fuel is consumed and appear biased to one side of the fit. To further validate these findings, additional large battery-electric aerial vehicles are required. Their analysis will help determine whether a secondary power law prevails or if, as mass increases, battery-electric vehicles coalesce with the rest. In addition, the inclusion of general aviation aircraft in future assessments may also provide new insights. However, for the present, a function parallel to the thermal fit, Equation (10a), intersecting the centroid of the battery-electric UAV data is depicted in green in Figure 7, presenting our conservative suggestion on how future battery-electric airplanes may behave in this representation.

5. Conclusions

In this work, our objective was to characterize and compare the capabilities of fixed-wing UAVs and airplanes. Threading the previous literature on range, speed, and transport efficiency, we reached a regression result that demonstrates, for the first time, a relationship between the maximum take-off mass and the useful energy of UAVs together with airplanes, connecting them across five orders of magnitude. Moreover, battery-electric UAVs, and potentially future battery-electric airplanes, are seen, for now, as a separate universe.

To reach this result, we investigated the estimated range and speed of UAVs and found them, at times, comparable to those of airplanes. We compared the transport efficiency of UAVs in two ways, namely, productive capacity and energy intensity. When based on productive capacity, we found UAVs competitive with airplanes, particularly turboprops. When compared using energy intensity, UAVs showed equivalent or better values against both trucks and airplanes. Comparing UAVs among the different powertrains under a useful energy scheme revealed different scaling dynamics between them, leading to a log-linear mathematical expression between mass and useful energy in the vehicle, adequately encompassing all but battery-electric and solar UAVs.

Considering that there are other flying UAVs, namely, rotary-wing, future work should attempt to analyze their characteristics compared to helicopters and from a useful energy perspective, as they have distinct particularities, such as hovering capability and, most often, a lack of lift surfaces for horizontal flight. Moreover, there are other unmanned solutions (ground vehicles and vessels) that could benefit from increased awareness and understanding compared to existing transport solutions.