In 1981, for example, Solar Challenger flew across the channel between England and France. Currently the most high-profile project is Solar Impulse, a team led by Swiss pilot Bertrand Piccard. He hopes to fly into the record books in 2014 by travelling around the world without using any fuel.
The team has already entered the record books after they built an aircraft that managed to stay aloft for 26 straight hours.
HB-SIA, as the one-man plane is known, has the mammoth wingspan of an Airbus A340, but with a tiny body that almost disappears under the wings. It packs 12,000 photovoltaic cells on to its wings, powering four 10 horsepower electric motors that are used to drive 3.5m diameter, twin-bladed propellers. But now the Solar Impulse team is working on a second-generation plane, ready for a 25-day global circumnavigation attempt, flying day and night.
“In the daytime he needs to charge his batteries with sunlight, and then during the night he should have enough energy to power the motors and fly on,” said Joern Juergens of SunPower, the company that supplies Solar Impulse’s solar cells.
“That is a real challenge.”
To increase the amount of energy it can collect, the new plane will have an extra 10,000 cells and a wingspan of 80m (262 ft), slightly wider than the wingspan of an Airbus A380, the largest passenger airliner in the world.
The plane will reportedly take off and land in the United Arab Emirates and will track the equator to maximize the amount of sun falling on its cells.
But the challenges don’t stop there.
The plane needs to be as lightweight as possible, which means a delicate balancing act between the numbers of batteries it needs to power the craft and the number it can carry.
The weight issue carries over to the pilot as well – meaning it can only have one.
As a result, the circumnavigation attempt will require at least five stops to change pilots.
It is this kind of extreme limitation that means nobody – including Piccard – will claim that Solar Impulse provides a practical blueprint for mass solar-powered air travel.
Instead, he says, Solar Impulse is a “demonstration craft”, aimed at highlighting how far renewable energy sources have come.
He has even admitted that the idea of a passenger plane may be impossible.
But, according to van der Linden, the curator at the Smithsonian, that should not stop people trying.
“Right now it’s more a novelty than anything else, but the idea of unlimited power is a wonderful promise and needs to be pursued,” says Bob.
“It’s free energy. You could fly a solar-powered sailplane, or motorised glider almost indefinitely.”
And even if the sun cannot be tapped directly, SunPower’s Juergens sees another way to harness the sun.
"If you use sunlight to produce hydrogen gas, you could run a plane on that, no problem."
His plan is to keep the solar cells on the ground and use them to create a clean, green liquid fuel for aircraft.
"You could use solar energy to produce the fuel for a 747 equivalent.
“You would have a large solar plant producing hydrogen. Then you would pump it into the plane, and the plane would fly."
You can hear Jon discuss the latest advances in science in Science in Action, every week on the BBC World Service.