Balancing Sunlight and Storage for Persistent Stratospheric Flight

High-altitude pseudo-satellites (HAPS) are lightweight, solar-powered aircraft designed to loiter in the stratosphere for weeks or months, providing services such as broadband connectivity, Earth observation, or disaster monitoring. Unlike conventional satellites, HAPS can be recovered and upgraded, yet they face a relentless daily energy challenge: collect enough solar power during daylight to propel the aircraft, operate payloads, and charge batteries for night-time flight. This calculator offers a transparent way to estimate whether a given configuration will achieve indefinite endurance or how long it can stay aloft before battery depletion.

The model begins with the fundamental energy balance. During daylight, solar panels generate power given by $\mathrm{P\_\{sun\}\; =\; A\; \backslash eta\; I}$, where $A$ is panel area, $\mathrm{\backslash eta}$ is efficiency, and $I$ is irradiance. Multiplying by daylight hours yields energy collected. Subtracting the energy needed to power the craft during daylight gives the surplus available to charge batteries. The batteries must then supply power through night hours. If the daily surplus equals or exceeds night consumption, the system can, in theory, fly indefinitely barring weather or component degradation.

Stratospheric conditions are ideal for solar collection: above most clouds, irradiance approaches 1,000 W/m², and temperatures are low. However, thin air necessitates large wingspans for lift, limiting structural mass available for batteries and payloads. Designers therefore seek optimal compromises. The calculator’s inputs reflect this: users specify panel area, efficiency, irradiance, battery capacity, power draw, and day/night durations, which vary with latitude and season.

The script computes several intermediate quantities. Daytime generation energy is $\mathrm{E\_d\; =\; P\_\{sun\}\; h\_d}$, while energy consumed over the entire day is $\mathrm{E\_c\; =\; P\_\{load\}(h\_d\; +\; h\_n)}$. Net daily balance is $\mathrm{\backslash Delta\; E\; =\; E\_d\; -\; E\_c}$. If $\mathrm{\backslash Delta\; E\; \backslash geq\; 0}$, the aircraft accumulates energy and can operate indefinitely provided batteries have sufficient capacity to handle night-time demands. If $\mathrm{\backslash Delta\; E\; <\; 0}$, the deficit drains the batteries, and endurance is limited to $\mathrm{T\; =\; \backslash frac\{E\_\{bat\}\}\{|\backslash Delta\; E|\}}$ days.

The explanation explores nuances of each parameter. Panel efficiency, once around 15%, now exceeds 30% for cutting-edge cells, but real-world values drop due to temperature and angle-of-incidence losses. Irradiance depends on season and latitude; at high latitudes, winter daylight may be only a few hours, severely limiting energy. Power draw encompasses propulsion, avionics, and payload; some missions may throttle payload operation at night to conserve energy. Battery capacity is constrained by weight; lithium-sulfur batteries promise higher specific energy, enabling longer endurance.

The discussion continues with operational strategies. Some HAPS missions adopt a “siesta” mode, climbing during the day and descending at night to reduce required lift power. Others use aerodynamic efficiency to glide when batteries wane. The narrative considers meteorological factors: stratospheric winds can force repositioning maneuvers, increasing power demand. A table summarizing calculated energy flows allows planners to test scenarios such as adding more solar area or reducing payload power.

Technological history enriches the explanation. Early pioneers like NASA’s Pathfinder and Helios programs demonstrated multi-day flights but suffered from structural failures and energy shortfalls. Modern projects—Airbus Zephyr, SoftBank’s HAPSMobile, and others—benefit from carbon-fiber structures and high-efficiency cells yet still wrestle with the tyranny of energy balance. The text recounts these case studies, illustrating how incremental improvements have extended endurance from days to months.

The calculator also addresses seasonal planning. For equatorial operations where day and night are each about 12 hours, parameters may be relatively stable. At mid-latitudes, day length swings dramatically, so operators may migrate platforms or adjust payload activity. An example shows that a craft with 100 m² of panels at 25% efficiency, drawing 5 kW continuously, generates 300 kWh during 12 hours of sunlight. After covering 60 kWh of daytime load, 240 kWh remain for charging batteries, easily meeting the 60 kWh needed for 12 hours of night. The surplus implies indefinite endurance if batteries can store at least 60 kWh. Reducing day length to 8 hours flips the balance, causing a deficit that drains a 200 kWh battery in roughly 3 days.

Beyond pure energy arithmetic, the explanation touches on regulatory and infrastructure considerations. HAPS operate at altitudes around 20 km, sharing airspace with few vehicles but requiring coordination with aviation authorities. Launch and recovery often occur in remote areas with favorable weather. The potential applications—from rural broadband to environmental monitoring—are vast, making endurance prediction essential for business cases. Operators need to know how many aircraft to deploy, when to schedule maintenance, and how seasonal solar variation affects service availability.

For educational use, the script’s simplicity invites modification. Students can extend it to include solar incidence angle as a function of latitude and day of year, or to model battery charge/discharge efficiencies. Because the code runs entirely in the browser, it serves as a starting point for deeper exploration into renewable-powered aviation. Ultimately, the calculator emphasizes that persistent flight hinges on a delicate balance: harvesting just enough sunlight to carry energy through the long, cold night.