Near-space solar-powered unmanned aerial vehicles (UAVs) have attracted extensive attention due to their uninterrupted cruise capability and have become a research hotspot in recent years [1
]. With the improvement of flight duration, the importance of flight profile and power spectrum simulation has become increasingly prominent.
Nowadays, the near-space solar-powered UAV has broken through the 24 h uninterrupted cruise technology. In 2005, the “Solong” UAV (the U.S.) became the first solar-powered UAV to achieve continuous flight for more than 24 h. However, the flight process is manually controlled, and thus it has no ability to carry out ultra-long flight time reconnaissance tasks [4
]. The “Zephyr-6” UAV (the UK) achieved 82 h and 37 min of continuous flight in 2007, creating a world record for the sustained flight time of a UAV [5
]. It conducted route planning through the navigation system and reduced the dependence on secondary batteries by using a gravity energy storage strategy. In 2016, the “Atlantisolar” UAV (Switzerland) carried out a 26 h continuous refugee search and rescue mission [6
]. Through a scientific route planning strategy, it conducted the task with maximum efficiency and provided a series of useful information for the rescue team. The “Owl” UAV (Russia) completed a 50 h non-stop flight test at an altitude of 9000 m in 2016, and its mission objective was to provide relay communications for the Arctic region [7
]. In 2022, Airbus’s “Zephyr-S” UAV extended the continuous flight duration record of solar-powered UAVs to 64 days. However, an accident that occurred during the final stage of the flight destroyed the aircraft. [8
] In addition, there is a large number of solar-powered UAVs in the research stage, such as the “Phase-35” UAV (the UK), the “Swift HALE” UAV (the U.S.), the “Sunglider” UAV (Japan), and the “Createv” UAV (Canada), all of which completed their first flight in 2020 [9
]. Although their scales are different, they all aim to achieve a longer flight time. The further extension of cruise time requires both high-precision subsystem modeling and flight profile simulation in a long working cycle.
Systematic mathematical and physical models are the basis for flight profile and power spectrum simulation. Noth [10
] first established the mathematical models of each subsystem of the solar-powered UAV, providing a reference for subsequent scholars to carry out the overall design of the solar-powered UAV. Colas et al. [11
] developed a conceptual multidisciplinary design framework for high-altitude long-endurance aircraft. In this framework, first-order physical models are widely used, and the reliance on historical empirical data is minimized. The simulation results have an appropriate level of fidelity while maintaining computational efficiency. Wang XY et al. [13
] built systematic mathematical and physical models for the modular solar-powered aircraft (M-SPA), including the energy model, the aerodynamic model, and flight environment settings. On this basis, the multi-phase flight mission strategy is designed by analyzing the energy consumption of flight mode.
The energy acquisition and consumption model of solar-powered UAVs is the core of mathematical and physical models. Wang CY et al. [14
] established a comprehensive energy acquisition model of solar-powered UAVs by combining the clear sky radiation model and the relationship between attitude, sun orientation, and the earth and built the energy consumption model of the steering gear and the propulsion system through experiments. On this basis, they compared the differences between aileron control and differential control in the aspects of operating efficiency and energy consumption. Dwivedi et al. [15
] developed the mathematical model for the available radiation at a specific geographical location on a given date and time in order to optimize the selection of battery and flight trajectory for a solar-powered aircraft. Wu et al. [16
] developed an optimal flight control approach for planning the flight path of sun-tracking solar aircraft within a mission region and derived the solar insolation model, power conversion model, power consumption model, and flight speed model of the Λ-shape solar-powered UAV. However, the above models all consider the performance indicators as fixed values and do not reflect the performance degradation under ultra-long task cycles.
Another important part of the mathematical and physical model is the performance attenuation model, which reflects the degradation of photovoltaic (PV) cell performance and the decline of secondary battery capacity. Ma DY et al. [17
] pointed out that the reason for the degradation of PV cell efficiency is that space radiation will introduce defects to the cell, leading to a reduction in the minority carrier’s life and changes in the electrical performance. Hu et al. [18
] combined the electron and proton energy spectrum and relative damage coefficient, equivalented the radiation effect of space-charged particles to the radiation of 1 MeV single energy particles, and predicted the performance change of triple-junction GaAs cells in the radiation environment of geosynchronous orbit. Yan et al. [19
] systematically studied the radiation damage law of triple-junction GaAs cells by means of spectral response, fluorescence spectrum, and other analysis methods and established the attenuation degradation model of this type of cells in different orbits. Moreover, the influence of the capacity attenuation of the secondary battery on mission feasibility also cannot be ignored. Liu et al. [20
] conducted a 0.5 C cycle discharge test on Li(NiCoMn)O2
soft pack lithium battery under the approximate vacuum pressure and found that the capacity decreased to 80% after 10 cycles. Mussa et al. [21
] studied the effect of external pressure on the cycle life of lithium-ion batteries and found that the pressure had little effect on the initial capacity but had a significant impact on the impedance and cycle life.
Based on the mathematical and physical model, the researchers developed the optimal flight path design of the solar-powered UAV, which is a special research content different from conventional aircraft [22
] and is also the basis of flight profile and power spectrum simulation. Klesh et al. [23
] introduced the concept of a power ratio (the ratio of absorbed power to consumed power) and studied the optimal trajectory of point-to-point missions. Wang et al. [24
] established the flight strategy optimization for high-altitude long-endurance solar-powered aircraft based on the Gauss pseudo-spectral method. The results indicate that proper changes in the attitude angle contribute to increasing the energy gained by PV cells, and the utilization of gravitational potential energy can partly take the role of a battery pack. The introduction of the gravity energy storage strategy [14
] reduced the dependence of the solar-powered UAV on the secondary battery and also brought uncertainty to the flight profile. Gao et al. [25
] ignored the influence of wind and propeller thrust and established the motion equation of the descending process of high-altitude solar-powered UAVs. The motion is limited in the longitudinal profile, and the optimal trajectory is obtained by using the Gauss pseudo-spectral method with the optimization goal of the longest gliding time in the unit height difference. By introducing the EFF parameter (flight time/total solar energy), the equivalence of gravity energy storage and electric energy storage was compared [26
], and the effects of solar radiation time, charging ratio of battery, energy storage density, and initial height on the equivalence were analyzed. Sachs et al. [27
] studied the minimum energy storage flight trajectory of solar-powered UAVs. The results show that by climbing in the daytime and gliding at night, it could theoretically achieve 24 h uninterrupted flight without secondary batteries. However, the maximum climb height during the day is more than 20 km, and the minimum glide height at night is only about 1 km.
On the basis of the optimal path planning theory, scholars have simulated the flight profile and power spectrum of solar-powered UAVs in a long mission period. Zhang et al. [28
] established an energy model of the solar aircraft in each flight stage and classified and discussed various flight situations in the evening glide stage. This research shows the typical flight profile and power spectrum shape of the solar-powered UAV on the two-dimensional plane, which is of engineering reference significance. Ma JC et al. [29
] developed a flight strategy for a solar-powered UAV and established a simulation model by using the Simulink toolbox. Finally, the flight profile within 72 h was obtained, and the results show that the strategy controlling the UAV to fly in a height range can optimize the efficiency of the solar power as well as save energy and enhance the long-flight stability of the UAV. Ma DL et al. [30
] studied the varied-height flight paths for solar-powered aircraft and their application based on the theory of gravity energy reservation and introduced the overall design method for a solar-powered UAV with varied-height paths. Huang et al. [31
] focused on the deployment problem of solar-powered UAVs used for communication services and proposed a nearest-neighbor-based navigation method to guide the movements of the UAVs.
There is still space for improvement on mathematical and physical models of subsystems, energy utilization, flight path programming, and mission profiles despite existing extensive studies. In this paper, the above space is explored and filled through modeling, simulation, experiment, and analysis. In Section 2
, the study object is introduced, and based on the test data obtained from a solar-powered UAV, the systematic mathematical and physical models of aerodynamic, energy, propulsion, and other subsystems are constructed. In Section 3
, on the basis of the principle of maximizing the utilization of light and minimizing electric energy consumption, the flight profile control strategy is proposed, and the energy balance equations of each flight stage are established. In Section 4
, the typical flight profile and power spectrum of solar-powered UAVs are obtained through simulation, and the key events in each stage are discussed. In Section 5
, the input parameters are decomposed into task indicators and performance indicators, and the effects of different indicators on flight profile and mission feasibility are studied respectively. The research methods and conclusions of this paper provide a theoretical basis and technical support for the overall design, route planning, and flight test of solar-powered UAVs.
4. Typical Flight Profile and Power Spectrum
Based on the mathematical and physical model in Section 2
and the flight strategy in Section 3
, the flight simulation is carried out, and the typical flight profile and power spectrum are obtained. During the simulation, the latitude of the solar-powered UAV is 41° N, and the flight date is 21 June. Figure 18
shows the flight altitude and speed of a typical flight profile. Figure 19
shows the climb rate at different times. The positive climb rate means that the UAV climbs upward. Figure 20
shows the charging and discharging curve of the secondary battery in the typical flight profile. The positive power indicates the battery charging. Figure 21
shows the power spectrum of a typical flight profile. At any time, the total required power of the UAV is not higher than the available power, and the power of the motor is not higher than its maximum continuous power.
On the first day, the solar-powered UAV takes off in the early morning. It is in the climbing phase from 4:00 to 17:10, and the climbing increases first and then decreases. This is because the radiation power is 0 when taking off, and the UAV climbs by fully using the energy of the secondary battery. At this moment, the power of the motor does not reach the maximum value. With the increase in the available solar power, the motor reaches the maximum power, and the UAV starts to climb at the maximum rate. At this moment, there is still available solar power, and the secondary battery is in a charged state until the SOC = 100%. Subsequently, the UAV is powered directly by PV cells to climb. As the altitude continues to increase, the required power for climbing increases and the illumination power decreases, so the climb rate decreases significantly and the UAV reaches the maximum altitude of 20 km at dusk.
From 17:10 to 19:40, the UAV is in the powered gliding phase. During this stage, the energy stored in the secondary battery is not used, and the PV cells directly power the motor, which is an important means to maximize the utilization of light energy. At this phase, the residual light is not enough to maintain the UAV in level flight. Therefore, although the propeller is still rotating, the altitude is falling. At 19:40, the light intensity is only enough to maintain the energy required for the airborne equipment, and the UAV stops the powered gliding phase.
From 19:40 to 22:20, the UAV is in the unpowered gliding phase, and it glides by relying on gravitational potential energy. At 19:40, the secondary battery begins to intervene in the flight, providing the power required by the equipment together with the remaining light. However, the secondary battery does not supply power to the motor at this stage. At 22:20, the UAV reaches the night flight altitude of 10,000 m, and it does not continue to glide. The lower altitude means a significantly enhanced wind field, so the solar-powered UAV usually does not conduct night flight below 10,000 m.
From 22:20 to 7:30 the next day, the UAV is in level flight. Before sunrise, the UAV completely relies on secondary battery power for level flight. After sunrise, with the increase in illumination power, the discharge power of the secondary battery gradually decreases until the illumination power can fully support level flight, and the discharge power of the battery decreases to 0. Subsequently, the remaining illumination power is used to charge the secondary battery until 7:30, when the battery charging power has reached the maximum value, while the illumination is still surplus. Then, the UAV climbs with the remaining light and begins the cycle flight of the new day.
As shown in Figure 20
, from the first day to the fourth day, the maximum value of SOC
decreased from 99.79% to 99.29%. Since the specified minimum SOC
value is not allowed to be lower than 10%, in order to ensure sufficient energy supply at night, the loss of secondary battery capacity can only be compensated by gravitational potential energy. As shown in Figure 18
, from the first day to the fourth day, the night cruise altitudes decreased from 10,000 m to 9911 m. It can be predicted that with the increase in the cycle number, the altitude of night flight will further decrease.