An engineer’s back-of-the-envelope calculations on Facebook’s Internet-providing solar-powered UAV.

By now you’ve probably heard about the Facebook Aquila, a solar assisted electric aircraft designed to bring Internet access to developing nations. Aquila is named after a constellation – ‘Aquila’ is Latin for ‘Eagle’ – so it’s fitting that Facebook plans to put a constellation of Aquilas (Aquilae?) in the air to form a communication network. A full-scale prototype is now ready, and engineers expect testing to get off the ground in late 2015.

As expected, Facebook isn’t releasing much technical information about the plane. We know it weighs about 400 kg (900 lbs), roughly one-third the weight of a Toyota Prius. Most of the weight is due to the carbon composite frame and the batteries; the “payload” (communication equipment) only weighs 23 kg (50 lbs). Its wingspan is 42m (138 ft), about the same as a Boeing 737. Because the Aquila is designed to fly at altitudes of 18 – 27 km (60,000 – 90,000 feet), well above commercial airliners and weather, the enormous wingspan is needed in order to maximize lift in very thin air.

See the announcement page for more about the structure and materials. I’m interested in the power system, but since they’re keeping that information to themselves, I’ll take an **educated guess** regarding the electric motors, photovoltaic panels, and battery capacity. I’ll use the Solar Impulse and the SolarStratos – two noteworthy solar powered aircraft – as references for comparison data.

## Power

**Solar Impulse:**

Wingspan: 63 m

Weight: 1600 kg

Total Motor Power: 30 kW (40 hp)

Power-to-Weight ratio: 19 W/kg

**SolarStratos:**

Wingspan: 20 m

Weight: 350 kg

Total Motor Power: 13 kW (18 hp)

Power-to-Weight ratio: 37 W/kg

**Aquila:**

Notice that the SolarStratos requires nearly twice as much power per unit of weight compared to the Solar Impulse, probably due to its shorter wingspan. The **Aquila’s 42 meter wingspan** falls roughly in the middle, so let’s assume that its power-to-weight ratio is about halfway between the others: around **30 W/kg**. (This is a ballpark estimate, so please forgive the heavy rounding.) That means the Aquila needs about **12 kW of power**, roughly 16 hp. Aquila uses four propellers, so we’ll assume each is driven by a 3 kw (4 hp) electric motor. In fact, Aquila probably needs even less power because it’s not designed to take off on its own; it will be lifted to cruising altitude by balloons, fly for about 90 days, and then glide to a landing. So let’s assume that the total motor power should be about 10 kW.

## Photovoltaic Array

The wingspan represents the actual width of the plane, not the combined length of the two wings themselves. Assuming a 30 degree sweep angle, a little geometry says that each wing is about 24m long, and a visual estimate suggests that each wing is about 2m wide. That’s 96 square meters of total wing surface area covered by PV panels. At 27 km, Aquila’s daytime altitude, the solar intensity is about 1300 watts per square meter. Assuming 20% efficient PV panels, the array could produce 25 kW of peak power. It’s probably even better since PV panels operate more efficiently at cold temperatures, but I’m ignoring losses in my estimates so we’ll call it even.

## Battery Bank

Given that 10 kW are used to run the motors, that leaves 15 kW going to the battery bank at peak times. It’s hard to estimate peak sun hours (PSH) for a moving vehicle at 27 km, since the tilt angle will vary, but since there’s no cloud cover up there, let’s call it 6.5 PSH. That’s 97 kWh of energy charging the batteries during the day, about the same as the Solar Impulse’s battery bank, and almost five times that of the SolarStratos.

At night the Aquila will drop to an altitude of 18 km, where the air is more dense, in order to conserve power. Denser air increases both lift and drag, but the craft was designed to maximize the lift-to-drag ratio, so it takes less power to fly in denser air. So instead of needing 10 kW, let’s call it 8 kW. If it draws 8 kW from the batteries for 12 hours, it will completely deplete the battery bank every night and fully charge it during the day.

**Remember that these are rough estimates, not exact figures**, so I’m not taking losses into account. I’m not trying to prove that it works, only to show that the numbers are in the right ballpark. It appears that they are. And I realize that I’m only calculating the power required to keep the plane flying, not the power to run its electronics. Like Google’s Loon, I’m certain that the payload’s power requirements are minuscule compared to the power needed to fly the aircraft.

## The Constellation

Also similar to the Loon, several Aquilas will operate as a constellation, covering a wider area. Each plane flies in a circle with a 50 km radius. A base station on the ground communicates with the “mother” Aquila, which uses lasers for air-to-air communication with other aircraft in the constellation. The lasers are capable of transmitting data at 10 Gbps – comparable to fiber optic speeds. From there, each Aquila will communicate with ground-based antennas using radio frequencies, providing WiFi access to anything in its range.

Here’s a video with more information:

What’s most amazing to me is that the engineering team designed this aircraft – pretty much from scratch – in about fourteen months. Maybe an engineering degree should be the minimum requirement for elected office.

^{Images and video courtesy of Facebook}