This section highlights the usability of the correlations and their implementation with existing methods for the design and performance assessment of electric and fuel-based UAVs.
5.1. Electric-Powered UAV
This example illustrates the application of the correlations in the performance assessment of battery-powered unmanned aircraft. The Skywalker X8 UAV was defined as the baseline case because it is one of the most used commercial UAVs for mapping and monitoring missions. In addition, the Skywalker UAV offers the typical performance of a small electric fixed-wing UAV; therefore, it is a good representative case of study. For this UAV, the effect of resizing the power source (i.e., battery) on the UAV performance was evaluated. According to Traub [
34], the endurance in straight level flight of a battery-powered aircraft can be calculated with Equation (
3), where
is the battery hour rating;
combines the motor and propeller efficiency in a single term;
V and
C are the rated voltage and battery capacity, respectively;
is the air density;
S is the wing reference area;
is the zero lift drag coefficient of the UAV;
W is the total UAV mass;
k is the induced drag factor; and
n is the discharge rate, which depends on the battery type and temperature. As observed in this equation, the endurance of a battery powered UAV depends greatly on the battery parameters such as the rated voltage, capacity, discharge rate, and of course the battery mass, which also affect directly to the total UAV mass
W. According to this equation, the endurance can be maximized by using batteries of higher capacity and voltage; however, this is not completely true because the battery mass
and consequently the total UAV mass
W is also increased proportionally to the battery capacity
, according to the correlations presented in
Table 2.
In a previous work [
49], we employed the proposed correlations to study the effect of resizing the power source of an existing UAV. A modified version of Equation (
3) was also developed based on experimental measurements of the power consumed by the propulsion system, avionics, and payload. Compared with Equation (
3), the modified endurance equation (Equation (
4)) introduces two terms: the effective battery capacity
and the power consumed by avionics and other electronics items
. The effective battery capacity is a fraction of the nominal capacity that can be employed for propulsion and the avionics power is the fraction of power that is diminished from the power source (i.e., the battery) to energize the electronic items on board the UAV, including payload, actuators, and avionics.
In Equations (
3) and (
4), the total UAV mass is as function of the battery mass
, considering the mass of the other components including the fuselage mass remain fixed. This exemplifies that the present correlations permit to formulate more detailed mass calculation approaches, as stated in the flowchart depicted in
Figure 2.
Table 6 presents the baseline parameters of the Skywalker X8 UAV, employed in this illustrative example. For this UAV, the effect of increasing the battery capacity on the UAV performance was evaluated by means of the two endurance equations discussed above. For this particular example, the correlation to determine the mass four cells (4S) Li-Po batteries were employed, since manufacturers recommend that the already installed electric motor works well with this type of batteries. The total UAV mass was calculated as function of the battery mass and the fixed mass, as mentioned above. As observed in
Figure 10, three payload mass were evaluated, which correspond to typical RGB cameras used for monitoring and mapping tasks. In this study, the total UAV mass was constrained to
[kg], since this is the maximum take-off mass recommended for this UAV. Therefore, this study concentrated on determining how much the battery capacity can be increased in order to boost the UAV endurance.
Figure 10 shows the effect of the battery capacity on the UAV endurance, determined through Equations (
3) and (
4). In this figure, the solid curved lines represent the UAV endurance determined with the original Equation (
3), for each of the three payload scenarios. The solid vertical lines indicate the maximum battery capacity to satisfy the constraint imposed for the total UAV mass. The dots that intersect with the curved lines delimits the maximum battery capacity and maximum endurance that can be achieved under the imposed considerations. The square and triangular markers indicate the maximum endurance and battery capacity, respectively. However, they were obtained with the modified endurance equation (Equation (
4)). As observed, the endurance estimations obtained with the original equation are very optimistic, while the values obtained with the modified equation are closer to actual endurance values, according to the authors experience with experimental flight tests.
The above example illustrates how the present correlations can be coupled with existing tools for the design and performance assessment of electric-powered aircraft. In the above example, the characteristics of the electric motor were kept fixed; however, in a more complicated case of study or design problem, the correlations to size the electric motor can be coupled easily with a detailed mass estimation model or even with a propeller performance model. This example demonstrates briefly the usability of the correlations for simple design cases and even for exploratory and optimization studies. Furthermore, their parametric nature permits implementing the correlations in any computational framework for UAV design and optimization.
5.2. Fuel-Powered UAV
This section exemplifies the use of the sizing correlations of internal combustion engines. The coupling between a propeller performance model, the engine sizing correlations, and the refined mass calculation is briefly explained. According to Gundlach [
13], the sizing process of a propeller-driven propulsion system begins with the assessment of the propeller performance to determine the propeller characteristics such as the advanced ratio
J, the power coefficient
, the propeller diameter
D, and the rotational speed. For this purpose, the actuator disk theory or the blade element momentum theory can be employed. With the propeller performance parameters, the power shaft can be determined with Equation (
5). This power shaft corresponds to the power that the internal combustion engine must supply to the propeller. At this point, the power shaft or power output (from the engine perspective) can be used to determine general but significant characteristics of an internal combustion engine that fulfills the thrust and power requirements. For this, the correlations presented in
Table 4 and
Table 5 can be employed. As appreciated, the correlations provided for internal combustion engines permit determining the engine mass and displacement as function of the power shaft or power output. In these correlations, the engine type is implicit, since correlations for two and four stroke engines were developed separately. The main advantage of using the present correlations is that they were derived from off-the-shelf components widely used in UAVs, which make them more suitable for the design and analysis of different UAV categories compared with existing correlations that have been derived for large civil aircraft.