# Solar planes are cool, but they’re not the future of flight

Have you heard of the Solar Impulse? It’s a Swiss aircraft that’s powered entirely by solar energy. The ambitious goal of this project is to fly around the world using only solar power. On May 1, they’ll begin a trip from San Francisco to New York City, with multiple stops along the way. They’ve already pulled off a 26 hour flight, as well as an inter-continental journey from Spain to Morocco, powered only by sunshine. (They use battery packs to store the spare energy and power the plane at night.)

When I first heard about this, I was kind of astonished that this is even possible. Are solar panels really sufficient to power an aircraft? And when can I expect to fly in one?

To find out how they managed to pull off this feat, let’s crunch some numbers.

### How much power can you get from the sun?

First, let’s work out how much power the plane captures from sunlight. The Solar Impulse has about the same wingspan as a 747 airplane, and its wings are covered in nearly 12,000 solar cells. That’s about 200 square meters of solar cells.

Now, the amount of power delivered by sunshine is a well known number. If you ignore clouds, and average over day and night, it comes to about 250 Watts delivered to every square meter of land. This number, 250 Watts/square meter is how much power we, sitting here on earth, can extract directly from the sun.

Put the two numbers together, and we get 250 Watts/square meter × 200 square meters = 50,000 Watts. This is the maximum amount of power that this airplane can theoretically capture from the sun, given its wingspan.

But we don’t have the technology to tap into all of this power. The best commercially available solar cells are about 20% efficient at capturing solar power, and then there are further losses in the batteries and the electric motors, all of which waste some power. Overall, the kind folks at Solar Impulse tell us that 12% of the incoming solar power is pumped out by the electric motors. That’s 12% of 50,000 Watts, leaving us with 6,000 Watts of useful power. Remember that number, we’ll come back to it.

### How much power do you need to fly a plane?

So far so good. On average, we’ve got 6,000 Watts being pumped out to fly this plane. But is that enough? To answer this, we need to figure out how much power it takes to fly a plane. There are really two components to answering this question.

1. Weight.

Heavier planes need more power to fly them. That’s because planes fly by throwing air downwards. They need to throw enough air downwards to counteract their own weight, so heavier planes need to ‘work harder’ on throwing air down. To stay afloat, a heavier plane needs to fly faster than a lighter plane, so it can ram into more air each second, and hurl the air downwards, counteracting its own tendency to drop out of the sky. (If you’d like to read more on how this works, see my post entitled Can we build a more efficient airplane? Not really, says physics.)

So it takes more power to fly a heavier plane. That’s pretty intuitive. (By the way, since we’re on the subject, this is also why it’s wrong to say something like “The plane was flying anyway, so my flying on it was carbon-neutral.” No – it takes extra energy to carry your extra weight! Not to mention that airlines would fly fewer planes if there were fewer people flying.)

But weight isn’t the whole story.

2. Aerodynamics, or the ability to glide.

Some planes are just better at staying up than others.  If I throw a paper airplane, it’ll glide across the room. If I take that same piece of paper, crush it into a ball, and throw it with same force, it won’t go nearly as far. The difference is that the paper airplane is more aerodynamic – it’s better able to throw air downwards and keep itself afloat. This is also why, if a 747 were to run out of fuel, it wouldn’t just fall out of the sky like a rock, but would glide about as effectively as a paraglider.

This ability to glide is captured by a number called the glide ratio. Here’s how it works. Imagine that you switch off the engines in a Boeing 747 mid-flight (don’t try this at home). It will end up falling 1 foot for every 12 feet that it moves forward. This means that it has a glide ratio of 12/1 = 12. An albatross glides 20 feet forward for every foot it falls (glide ratio of 20), while a sparrow glides 4 feet forward for every foot of descent (glide ratio of 4). Here’s a table of some more examples.

The larger the glide ratio, the more energy-efficient the airplane, because it means that you have more lift and less drag. Think of the albatross versus a sparrow. The most straightforward way of increasing your glide ratio is by increasing your wingspan, because then you can throw a lot more air down.

Let’s put these two concepts together. A heavier plane (more weight) consumes more energy to fly. A more aerodynamic plane (higher glide ratio) consumes less energy to fly. Divide those two numbers – the weight and the glide ratio – and voilà You’ve just found out how much energy it takes to fly a plane a certain distance.

This equation captures a simple idea. The total energy that it takes to fly depends on a plane’s weight, and is inversely related to its ability to glide. If you wanted to build an energy-efficient airplane, you’d want to make it really light, and have a large glide ratio. This is exactly what the Solar Impulse pulls off with a very light body and a huge wingspan. It’s quite a technical feat to balance these opposing demands. You could call it the albatross’s dilemma.

Now, the equation above tells you how much energy it takes to fly a certain distance. To convert this into a power rating, you need to multiply it by the speed of the plane.

The power consumed by a plane depends essentially on three numbers – its speed, its weight, and its glide ratio.

We’re finally ready to plug in the numbers for the Solar Impulse. The mass of the plane is 1600 kg, which corresponds to a weight of 15,680 Newtons (to go from kilograms to weight on Earth, you have to multiply by the conversion factor of 9.8 Newtons/kg). The glide ratio of the Solar Impuse is 40. How about the speed? Their website tells us that it has an average flying speed of 43 miles per hour, which is about 19 meters/second.

Plugging the numbers into our equation, we get that the total power needed to fly this plane is about 7,500 Watts.

Uh-oh.

Remember the 6,000 Watts of power that we got from the solar panels? The plane seems to consume more power than it produces. Our model predicts that plane doesn’t have enough power to stay up in the air. But this contradicts experiment – we know that this plane is able to fly. What’s going wrong?

Here’s what I think happened. I suspect the average speed that they offer on the website is a tad on the high side. Perhaps they measured this during a daytime flight, when the solar power is twice as high as the day-and-night average? I don’t know. Instead, let’s get the average speed from real flight data. In particular, the New York Times reports that for the Solar Impulse’s 26 hour voyage (day and night), it flew at an average speed of 26 miles/hour (nearly 12 meters/second).

Plug that number in, and you get a power consumption of 4,700 Watts. That’s safely within the 6,000 Watts that the solar panels can produce. Phew.

In reality, this number could be a little higher because the plane might have met some headwind along the way. And there are some assumptions in our calculation that put our estimate on the lower side of things (I assumed that the plane is flying at its most energy-efficient speed, and didn’t take into account the extra energy for takeoff and landing). But even with wiggle room of 25%, it’s less than 6000 Watts. The plane isn’t going to run out of juice, unless it meets some clouds or some serious tailwind.

In summary, we reasoned our way through a quantitative estimate of the power production and consumption of a solar-powered plane. Happily, the two numbers match. This sort of back-of-the-envelope calculation is what physicists call a toy model – you leave out the nitty-gritty details, and strip a problem down to its bare essentials. If it works, you can get a lot of insight with not a whole lot of work. For example, we didn’t need to delve into any hairy details of fluid dynamics, or get bogged down in drag coefficients of an airplane, the physics of solar cells, and so on. Yet we were able to make a reasonable, testable prediction.

### So, when do I get my solar plane?

Before we get ahead of ourselves and envision a world where we can zip around in our carbon neutral planes, let’s think of a few issues, and see what physics has to say about them.

1. Scalability. As we’ve seen above, the reason this plane can run on solar power is because it’s light and it has a large wingspan. Could we ever get this to work on a more practical scale – could we build a solar-powered equivalent of a 747? No – because carrying more people would mean that you’d have to increase the weight of the plane, and so you’d need more power to fly. But the amount of power you can provide is limited by the solar panels on the wings, so you just won’t be able to meet the demand. Replacing solar panels with more efficient panels won’t help much either – that can buy you energy gains of up to a factor of 2 or so, and that isn’t nearly sufficient to cope with the added weight.

2. Speed. This is one of the biggest limiters – the Solar Impulse will fly across the US at something like 30 or 40 miles per hour.

Planes are typically optimized to fly at the speed that minimizes fuel consumption. It turns out that the lighter the plane and the longer the wingspan, the slower this optimum speed. I’ve argued that solar planes have to stay light and have a large wingspan, so the physics of flight demands that they must fly slowly as well. If you try and speed up a plane past its optimum speed, you’ll have to spend a lot more energy on pushing air out of the way (drag forces).

This isn’t good news for our solar powered plane. If we’re stuck at highway speeds, we might as well just take a train, or a bus. (Here’s an interesting fact – it would cost about the same amount of energy per mile if you took all the people in a 747 and put them in cars, with two people in each car.)

3. Range. The range of a plane is the maximum distance it can go without re-fuelling. You might imagine that bigger planes always have a larger range because they have more fuel, but this isn’t correct, because they’re also heavier, and so they need to use their fuel faster. It turns out that there’s a maximum range that a plane (or a bird) can attain, and it depends on its glide ratio and on the energy density of the fuel.

Energy density is just a number that tells you how much energy you can get out of a kilogram of fuel. Gasoline has an energy density of 40 million Joules/kg = 40 MJ/kg. Plugging in the numbers for a gasoline powered plane gives a maximum range of about 13,000 km. This is about the distance from the USA to India, and there are direct flights that take you that distance.

If you could always fly in the sunshine, solar planes would have an unlimited range. But solar planes have to rely on batteries to fly at night, and this is what limits their range.

The most energy dense batteries around today are Zinc-air batteries, and they have an energy density of about 1.6 million Joules/kg = 1.6 MJ/kg. The Solar Impulse uses Lithium-ion batteries that are about half as energy dense. Plugging in the numbers for Zinc-air batteries gives a range of about 1,000 km, or about a fifth of the distance from San Francisco to New York – this is the furthest that a solar plane can fly in a night! Incidentally, this explains why the Solar Impulse needs to make so many stops to fly from San Francisco to New York. Of course, things may change if we develop phenomenally more energy dense batteries, but we’re still a long, long way from the energy density of gasoline.

Betrand Piccard, co-founder and co-pilot of Solar Impulse, was asked at a press conference whether solar energy would every power mainstream aircrafts. His response:

“It would be crazy to answer yes and stupid to answer no. Today we couldn’t have a solar-powered plane with 200 passengers. Maybe one day.”

Sadly, we still have a long way to go in building a viable, greener alternative to conventional flight. In another blog post, I’ve argued that it isn’t even possible – commercial airplanes are about as energy efficient as they’re ever going to get. The Solar Impulse is certainly an impressive technical feat, and it gets us to think more clearly about what really matters when it comes to building a better airplane.

References:

If you’d like to dig deeper into the math behind these arguments, check out this technical chapter in David Mackay’s book.

His immensely readable book Sustainable Energy – without the hot air is the best resource I’ve seen for thinking clearly and quantitatively about renewable energy.

I’ve previously written on the topic of airplane efficiency. Can we build a more efficient airplane? Not really, says physics.

• ScienceSalsa

Great post! I wonder if they used their plane as an airplane or as a glider; going from thermal to thermal. The Internet tells me you may have an average speed of 50-55 mph using that method.

• Fly guy

It’s frustrating to hear from people that are so poorly versed in technology and yet they don’t realize it. Even if you could capture and use all 50,000 watts of energy that is hitting this wing (if the sun was always shining straight down on it, which it is not) that is only about 70 horse power. The engines on a small commercial jet like a 737 create the equivalent of over 30,000 HP each! You can talk about higher efficiency all you want, but it takes huge amounts of power to go at jet speeds.

• Good post! Just a silly question on units… Glide ratio seems to be a unit-free quantity, so how is energy/distance=weight/glide ratio?

• Because energy = force × distance, so the units work out. (A Joule/meter is the same as a Newton)

• Ah, yes, very silly indeed. Thought of weight=mass. Blame it on the jet-lag? Anyway, great post (if a bit discouraging…)

• Benjohn

Great stuff, thank you!

I’m not sure if we’ll ever “green” transport planes, but if we do, I’m pretty sure the approach won’t be to slap solar panels all over them. It seems like it would make far more sense to use an energy dense fuel as we do now, and provide this fuel from a sustainable source (like turning algae in to fuel).

[aside – are flying things fairly unique in their extreme need for energy dense fuel?]

Where I can see this technology being useful is when something light needs to remain airborne indefinitely, probably over the same location. So, drones, basically. Not necessarily just military surveillance: they could be a platform for communications or environmental monitoring.

• That’s a far more reasonable (and potentially attainable) solution!

Flying things are certainly not unique in their need for energy dense fuel. A car uses the same amount of fuel per person as a plane does, assuming two people in the car. But unlike planes, there are no basic physics reasons why cars can’t be improved. (David MacKay has a great discussion of this in his book). Also since renewables like wind and solar are not always available, we need increasingly energy dense batteries to store their energy.

• Does it really make sense to use the average daily insolation? Wouldn’t it be better, for proof-of-concept purposes, to use the insolation that plane can expect during the day? Also, is the insolation notably different in the high troposphere compared to the earth’s surface? I feel like we’d get a better sense of how one of these bad boys can actually perform, during the day time, if we used a day-time average @ 30,000 feet, rather than a 24 hour average @ the-entire-Earth’s-surface. But maybe it doesn’t make a difference.

• Taurus Londono

“I’ve argued that it isn’t even possible”

Unwise, Aatish.

Of course more efficient panels will help, as will organic battery membrane potential. Do you seriously discount the possibility of a viable commercial airliner employing a hybrid power system that utilizes an outer layer of ultra-efficient photovoltaics (ie extended to infrared, based on quantum dots)?

When you say that more efficiency “doesn’t help,” you sound a bit silly.

Piccard has it right-
“It would be crazy to answer yes and stupid to answer no.”

• Taurus Londono

FWIW,

Mackay is right about contemporary engine technology and fuel efficiency. He’s not seeing the forest for the trees, however, if he doesn’t appreciate the energy efficiency encountered in life sciences; eg oxidative phosphorylation. If you think that the underpinnings of this molecular machinery will not ultimately be applied in various technologies, I suggest that’s a bet you’d lose.

• I may sound silly or stupid to you, but what part of the arithmetic do you disagree with? I’m making claims based on numbers, not just throwing out my own opinion. If you can do the same with your own claims it would be easier for me to take them seriously.

It’s quite clear from the article that I’m talking about a plane that gets all of its energy from solar power, not a ‘hybrid’ (what does that even mean? That it uses gasoline and solar power?). To scale a solar plane to 747 carrying capacities, we are talking about a 100 fold increase in weight capacity, and a 10 fold increase in speed. That’s an overall 1000 fold increase in power requirements. Even if you had 100% efficient photovoltaics, which you obviously can’t have, so you are capturing *all* the solar energy striking your wings, you would only get a 10X boost in power production. So, yes, I am seriously discounting the possibility of a purely solar powered viable commercial airliner, no matter how efficient your photovoltaics.

And power needs aside, such a plane would be severely limited by its range at night because of the energy density of even the most modern batteries, as I’ve argued in the article.

• Taurus Londono

It’s not that I “disagree” with the arithmetic, it’s that I disagree that your broad conclusions *necessarily* follow.

We already have the technology to store 0.2 farads per cm^2 using synthetic membranes. I can’t take seriously the prospect that aircraft of the foreseeable future will not utilize solar cells (even if they don’t derive *all* their energy from solar power).

Of course there’s nothing wrong with your arithmetic! What’s wrong is that you evidently can’t conceive of future advances in battery technology that might allow for a viable commercial passenger aircraft that could justifiably be called a “solar plane.”

I don’t assert that such a thing *will* exist, I only say that, given what we definitely know, it seems (extremely) unwise to claim that it will *never* exist let alone that it’s “impossible”. I’d just hate to see your blog entries end up as the early 21st century equivalent of mathematically credible dismissals of powered flight or space travel being handed down by esteemed scientific institutions.

• Brooks Nelson

I would agree with Taurus, though no commercial plane is likely to ever get much power from solar or from the batteries they charge they could reduce fuel consumption. (Always a good thing.) And while planes are parked at airports they could power the airport and potentially add to the nearby grid.

• Anindya Roy

I agree with Benjohn below – aircrafts built of smart materials (lighter but strong, better than the metal alloys presently used) fuelled by bio-kerosene may be the next best available green flying technology. Batteries have issues – after all it’s the Li batteries that grounded the Dreamliner, not its flight technology. Making the battery energy density comparable to gasoline’s is not around the corner… On the other hand, if we are talking about next big revolution of transporting people – fast and in a fuel efficient way – we may start toying with crazy ideas such as pods travelling through continent-long vacuum tubes, or a third rail on interstates to enable cars run on electricity with a good in-car battery pack for city roads…

• Alan Bell

How about with a much bigger wingspan? Like hundreds of meters longer. Basically a huge flying wing with quite a lot of props and quite a lot of wheels for landing and takeoff when the wing would sag. In the air it would have more power from a much bigger solar capture area. I think the future of this kind of thing for scale up is actually the hybrid heavier than air blimp covered in photovoltaics rather than fixed wing aircraft, but I can’t see why this can’t scale if you are not constrained by wingspan.

• That’s a great question. I would argue that you are indeed constrained by wingspan. The reason is that while longer wings give you more lift, they also weigh more, and lead to more drag. So plane designers need to optimize the wingspan for maximum fuel efficiency, to strike a balance between lift, drag and weight. Also, large wings reduce your ability to maneuver effectively (for the same reason that a tightrope walker carries a huge stick – the large moment of inertia decreases their angular speed.)

• I believe you are far to pessimistic about what solar panels and batteries will be able to offer within the next ten years. Solar panels that are only 50% efficient would double the performance of this aircraft and will be available sooner than you may think. Battery energy density will surpass fuel tanks within this decade…

• trans

Nuclear Isomers

• Justin

I’d just like to mention that the underlying goal of the Solar Impulse is to bring awareness and induce positive emotions towards renewable energies.

• comfrey

graphene?

• ganesshkumar

I going to look into the possibility of increase in solar power efficiency(which is 20% currently, as you mentioned) in future.

• brendan

maybe it would be interesting to work backwards. What would be a commercially viable number of passengers for a short-haul light aircraft. 10? What weight and wingspan does this imply? And minimum speed – maybe 80mph? We could use these assumptions to see what energy is required and so see what percentage contribution solar power could make to a daytime flight (i could do it here but am too lazy). How much does latitude, altitude and time of year change the equation? Could the rest of the power be supplied by batteries that were charged on the ground (perhaps covering the aircraft hangars in solar panels, or just using grid electricity)?

• WannabeMaxwell

Great post! I’m relatively new to Empirical Zeal, so I’m not sure about this: how often do you post new content?
Also, on another topic- in school, we’re all making a blog and I decided to make one on science. Do you have any advice/tips for me :)?

• Hi there. I’m basically on a blogging hiatus as I work on finishing my PhD thesis. After this summer, I’ll be back to a more frequent schedule. As for advice, I’d say write about something that you’re really excited about. Write how you’d speak. Write the sort of stuff that you’d love to read. I started by imitating the styles of other science writers, as it takes some time to get into your own groove. And get on to twitter where you can share your work, build your audience, and learn about how people respond to writing. It’s slow, patient work, but it’s fun, and very satisfying when something you write gets a conversation going.

• Fantastic post: educational in physics and environmental zeal. Thank you. I’m going to turn my 13 year-old son on to this site.

• Excellent! Thanks.